library(readr)
library(SciViews)
library(scatterplot3d)
library(car)
## Loading required package: carData
library(GGally)
## Loading required package: ggplot2
## Registered S3 method overwritten by 'GGally':
##   method from   
##   +.gg   ggplot2
library(lattice)
library(ggplot2)
library(ggridges)
library(ggvis)
## 
## Attaching package: 'ggvis'
## The following object is masked from 'package:ggplot2':
## 
##     resolution
library(ggthemes)
library(cowplot)
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## Attaching package: 'cowplot'
## The following object is masked from 'package:ggthemes':
## 
##     theme_map
library(gapminder)
library(gganimate)
## No renderer backend detected. gganimate will default to writing frames to separate files
## Consider installing:
## - the `gifski` package for gif output
## - the `av` package for video output
## and restarting the R session
## 
## Attaching package: 'gganimate'
## The following object is masked from 'package:ggvis':
## 
##     view_static
library(dplyr)
## 
## Attaching package: 'dplyr'
## The following object is masked from 'package:car':
## 
##     recode
## The following objects are masked from 'package:stats':
## 
##     filter, lag
## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union
library(tidyverse)
## ── Attaching packages
## ───────────────────────────────────────
## tidyverse 1.3.2 ──
## ✔ tibble  3.1.8     ✔ stringr 1.5.0
## ✔ tidyr   1.3.0     ✔ forcats 1.0.0
## ✔ purrr   1.0.1     
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library(grid)
library(gridExtra)
## 
## Attaching package: 'gridExtra'
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## 
##     combine
library(RColorBrewer)

wholesale <- read_csv("/Users/rutwik/Desktop/RBS/Sem 2/Multivariate Analysis/Wholesale customers data.csv")
## Rows: 440 Columns: 7
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (1): Channel
## dbl (6): Fresh, Milk, Grocery, Frozen, Detergents_Paper, Delicassen
## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
dim(wholesale)
## [1] 440   7
names(wholesale)
## [1] "Channel"          "Fresh"            "Milk"             "Grocery"         
## [5] "Frozen"           "Detergents_Paper" "Delicassen"
str(wholesale)
## spc_tbl_ [440 × 7] (S3: spec_tbl_df/tbl_df/tbl/data.frame)
##  $ Channel         : chr [1:440] "Retail" "Retail" "Retail" "Horeca" ...
##  $ Fresh           : num [1:440] 12669 7057 6353 13265 22615 ...
##  $ Milk            : num [1:440] 9656 9810 8808 1196 5410 ...
##  $ Grocery         : num [1:440] 7561 9568 7684 4221 7198 ...
##  $ Frozen          : num [1:440] 214 1762 2405 6404 3915 ...
##  $ Detergents_Paper: num [1:440] 2674 3293 3516 507 1777 ...
##  $ Delicassen      : num [1:440] 1338 1776 7844 1788 5185 ...
##  - attr(*, "spec")=
##   .. cols(
##   ..   Channel = col_character(),
##   ..   Fresh = col_double(),
##   ..   Milk = col_double(),
##   ..   Grocery = col_double(),
##   ..   Frozen = col_double(),
##   ..   Detergents_Paper = col_double(),
##   ..   Delicassen = col_double()
##   .. )
##  - attr(*, "problems")=<externalptr>
var(wholesale)
## Warning in var(wholesale): NAs introduced by coercion
##                  Channel     Fresh     Milk  Grocery   Frozen Detergents_Paper
## Channel               NA        NA       NA       NA       NA               NA
## Fresh                 NA 159954927  9381789 -1424713 21236655       -6147825.7
## Milk                  NA   9381789 54469967 51083186  4442612       23288343.5
## Grocery               NA  -1424713 51083186 90310104 -1854282       41895189.7
## Frozen                NA  21236655  4442612 -1854282 23567853       -3044324.9
## Detergents_Paper      NA  -6147826 23288343 41895190 -3044325       22732436.0
## Delicassen            NA   8727310  8457925  5507291  5352342         931680.7
##                  Delicassen
## Channel                  NA
## Fresh             8727310.0
## Milk              8457924.8
## Grocery           5507291.3
## Frozen            5352341.8
## Detergents_Paper   931680.7
## Delicassen        7952997.5
# Since it forces NA, lets take the first column which is survivorship out


cov(wholesale[, c("Fresh", "Milk", "Grocery", "Frozen", "Detergents_Paper","Delicassen")])
##                      Fresh     Milk  Grocery   Frozen Detergents_Paper
## Fresh            159954927  9381789 -1424713 21236655       -6147825.7
## Milk               9381789 54469967 51083186  4442612       23288343.5
## Grocery           -1424713 51083186 90310104 -1854282       41895189.7
## Frozen            21236655  4442612 -1854282 23567853       -3044324.9
## Detergents_Paper  -6147826 23288343 41895190 -3044325       22732436.0
## Delicassen         8727310  8457925  5507291  5352342         931680.7
##                  Delicassen
## Fresh             8727310.0
## Milk              8457924.8
## Grocery           5507291.3
## Frozen            5352341.8
## Detergents_Paper   931680.7
## Delicassen        7952997.5
#Taking a subset by survivorship of birds 
cov(subset(wholesale, Channel == "Retail")[,c("Fresh", "Milk", "Grocery", "Frozen", "Detergents_Paper","Delicassen")])
##                     Fresh     Milk     Grocery    Frozen Detergents_Paper
## Fresh            80779016 20601490   9760788.2 4374357.2        1299662.1
## Milk             20601490 93695263  78210648.1 3060973.3       37873911.2
## Grocery           9760788 78210648 150487093.2  991647.7       71297033.1
## Frozen            4374357  3060973    991647.7 3286257.1         192021.0
## Detergents_Paper  1299662 37873911  71297033.1  192021.0       39577809.6
## Delicassen        4884133  6493880   3797502.0 1119771.4         840085.8
##                  Delicassen
## Fresh             4884133.3
## Milk              6493880.5
## Grocery           3797502.0
## Frozen            1119771.4
## Detergents_Paper   840085.8
## Delicassen        3817322.9
cov(subset(wholesale, Channel == "Horeca")[,c("Fresh", "Milk", "Grocery", "Frozen", "Detergents_Paper","Delicassen")])
##                      Fresh     Milk  Grocery     Frozen Detergents_Paper
## Fresh            191315579 14840389 11556901 26211464.1        -113871.0
## Milk              14840389 18941345  9298710 10043354.7        1200992.1
## Grocery           11556901  9298710 12570665  5176321.0        2145355.2
## Frozen            26211464 10043355  5176321 31853748.3        -194428.2
## Detergents_Paper   -113871  1200992  2145355  -194428.2        1219022.8
## Delicassen        11080782  8624927  4986764  7608778.3         270277.7
##                  Delicassen
## Fresh            11080781.6
## Milk              8624927.4
## Grocery           4986763.8
## Frozen            7608778.3
## Detergents_Paper   270277.7
## Delicassen        9906296.2
# Take the correlation
cor(wholesale[, c("Fresh", "Milk", "Grocery", "Frozen", "Detergents_Paper","Delicassen")])
##                        Fresh      Milk     Grocery      Frozen Detergents_Paper
## Fresh             1.00000000 0.1005098 -0.01185387  0.34588146       -0.1019529
## Milk              0.10050977 1.0000000  0.72833512  0.12399376        0.6618157
## Grocery          -0.01185387 0.7283351  1.00000000 -0.04019274        0.9246407
## Frozen            0.34588146 0.1239938 -0.04019274  1.00000000       -0.1315249
## Detergents_Paper -0.10195294 0.6618157  0.92464069 -0.13152491        1.0000000
## Delicassen        0.24468997 0.4063683  0.20549651  0.39094747        0.0692913
##                  Delicassen
## Fresh             0.2446900
## Milk              0.4063683
## Grocery           0.2054965
## Frozen            0.3909475
## Detergents_Paper  0.0692913
## Delicassen        1.0000000
#Taking a subset by survivorship of birds 
cor(subset(wholesale, Channel == "Retail")[,c("Fresh", "Milk", "Grocery", "Frozen", "Detergents_Paper","Delicassen")])
##                       Fresh      Milk    Grocery     Frozen Detergents_Paper
## Fresh            1.00000000 0.2368048 0.08852909 0.26848139       0.02298557
## Milk             0.23680482 1.0000000 0.65865416 0.17444156       0.62194998
## Grocery          0.08852909 0.6586542 1.00000000 0.04459201       0.92383828
## Frozen           0.26848139 0.1744416 0.04459201 1.00000000       0.01683728
## Detergents_Paper 0.02298557 0.6219500 0.92383828 0.01683728       1.00000000
## Delicassen       0.27813701 0.3433729 0.15844150 0.31615435       0.06834682
##                  Delicassen
## Fresh            0.27813701
## Milk             0.34337291
## Grocery          0.15844150
## Frozen           0.31615435
## Detergents_Paper 0.06834682
## Delicassen       1.00000000
cor(subset(wholesale, Channel == "Horeca")[,c("Fresh", "Milk", "Grocery", "Frozen", "Detergents_Paper","Delicassen")])
##                         Fresh      Milk   Grocery      Frozen Detergents_Paper
## Fresh             1.000000000 0.2465271 0.2356607  0.33576532     -0.007456451
## Milk              0.246527128 1.0000000 0.6026126  0.40887741      0.249936011
## Grocery           0.235660662 0.6026126 1.0000000  0.25867937      0.548042398
## Frozen            0.335765322 0.4088774 0.2586794  1.00000000     -0.031201333
## Detergents_Paper -0.007456451 0.2499360 0.5480424 -0.03120133      1.000000000
## Delicassen        0.254530348 0.6296430 0.4468729  0.42833050      0.077776542
##                  Delicassen
## Fresh            0.25453035
## Milk             0.62964300
## Grocery          0.44687289
## Frozen           0.42833050
## Detergents_Paper 0.07777654
## Delicassen       1.00000000
#column means
#For Retail
colMeans(subset(wholesale, Channel == "Retail")[,c("Fresh", "Milk", "Grocery", "Frozen", "Detergents_Paper","Delicassen")])
##            Fresh             Milk          Grocery           Frozen 
##         8904.324        10716.500        16322.852         1652.613 
## Detergents_Paper       Delicassen 
##         7269.507         1753.437
#For Horeca
colMeans(subset(wholesale, Channel == "Horeca")[,c("Fresh", "Milk", "Grocery", "Frozen", "Detergents_Paper","Delicassen")])
##            Fresh             Milk          Grocery           Frozen 
##       13475.5604        3451.7248        3962.1376        3748.2517 
## Detergents_Paper       Delicassen 
##         790.5604        1415.9564
# ggplot
#Using ggplot to plot different variables against Channel of the annual spending
ggplot(wholesale, aes(x=Channel,y=Fresh)) + geom_point(aes(color=Channel))

ggplot(wholesale, aes(x=Channel,y=Milk)) + geom_point(aes(color=Channel))

ggplot(wholesale, aes(x=Channel,y=Grocery)) + geom_point(aes(color=Channel))

ggplot(wholesale, aes(x=Channel,y=Frozen)) + geom_point(aes(color=Channel))

ggplot(wholesale, aes(x=Channel,y=Detergents_Paper)) + geom_point(aes(color=Channel))

ggplot(wholesale, aes(x=Channel,y=Delicassen)) + geom_point(aes(color=Channel))

ggplot(wholesale, aes(x=Fresh, y=Milk)) + geom_point(aes(color=Channel))

ggplot(wholesale, aes(x=Fresh,y=Milk)) + xlim(0,100000) + geom_point(aes(color=Channel), pch=17) + 
  labs(x="Annual spending (m.u.) on Fresh products (Continuous)", y="Annual spending (m.u.) on Milk products (Continuous);", title="Wholesale Customer Data") 
## Warning: Removed 1 rows containing missing values (`geom_point()`).

# bar chart
ggplot(wholesale, aes(Fresh)) + geom_bar(position="stack",aes(color=Channel)) 

ggplot(wholesale, aes(Milk)) + geom_bar(position="stack",aes(color=Channel))

ggplot(wholesale, aes(Grocery)) + geom_bar(position="stack",aes(color=Channel))

ggplot(wholesale, aes(Frozen)) + geom_bar(position="stack",aes(color=Channel))

ggplot(wholesale, aes(Detergents_Paper)) + geom_bar(position="stack",aes(color=Channel))

ggplot(wholesale, aes(Delicassen)) + geom_bar(position="stack",aes(color=Channel))

ggplot(wholesale, aes(Fresh)) + facet_grid(.~Channel) + geom_bar(position="dodge",aes(color=Channel))

ggplot(wholesale, aes(Milk)) + facet_grid(.~Channel) + geom_bar(position="dodge",aes(color=Channel))

ggplot(wholesale, aes(Grocery)) + facet_grid(.~Channel) + geom_bar(position="dodge",aes(color=Channel))

ggplot(wholesale, aes(Frozen)) + facet_grid(.~Channel) + geom_bar(position="dodge",aes(color=Channel))

ggplot(wholesale, aes(Detergents_Paper)) + facet_grid(.~Channel) + geom_bar(position="dodge",aes(color=Channel))

ggplot(wholesale, aes(Delicassen)) + facet_grid(.~Channel) + geom_bar(position="dodge",aes(color=Channel))

# histogram
ggplot(wholesale, aes(Fresh))+geom_histogram(aes(color=Channel))
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

ggplot(wholesale, aes(Milk))+geom_histogram(aes(fill = after_stat(count)))
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

ggplot(wholesale, aes(Grocery))+geom_histogram(aes(fill = after_stat(count)))
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

# violin plot 
ggplot(wholesale, aes(x=Channel, y=Fresh)) + geom_violin(aes(color=Channel))

ggplot(wholesale, aes(x=Channel, y=Milk)) + geom_violin(aes(color=Channel))

ggplot(wholesale, aes(x=Channel, y=Grocery)) + geom_violin(aes(color=Channel))

ggplot(wholesale, aes(x=Channel, y=Frozen)) + geom_violin(aes(color=Channel))

ggplot(wholesale, aes(x=Channel, y=Detergents_Paper)) + geom_violin(aes(color=Channel))

ggplot(wholesale, aes(x=Channel, y=Delicassen)) + geom_violin(aes(color=Channel))

# box plot
ggplot(wholesale, aes(x=Channel, y=Fresh)) + geom_boxplot(aes(color=Channel))

ggplot(wholesale, aes(x=Channel, y=Milk)) + geom_boxplot(aes(color=Channel))

ggplot(wholesale, aes(x=Channel, y=Grocery)) + geom_boxplot(aes(color=Channel))

ggplot(wholesale, aes(x=Channel, y=Frozen)) + geom_boxplot(aes(color=Channel))

ggplot(wholesale, aes(x=Channel, y=Detergents_Paper)) + geom_boxplot(aes(color=Channel))

ggplot(wholesale, aes(x=Channel, y=Delicassen)) + geom_boxplot(aes(color=Channel))

# density plot and ggridges
ggplot(wholesale, aes(x=Fresh, fill=Channel, color=Channel)) + geom_density(alpha=0.3, aes(y=..scaled..)) 
## Warning: The dot-dot notation (`..scaled..`) was deprecated in ggplot2 3.4.0.
## ℹ Please use `after_stat(scaled)` instead.

# hexbin
ggplot(wholesale, aes(x=Fresh, y=Channel)) + geom_hex(aes(color=Channel)) 

cor(wholesale[, c("Fresh", "Milk", "Grocery", "Frozen", "Detergents_Paper","Delicassen")])
##                        Fresh      Milk     Grocery      Frozen Detergents_Paper
## Fresh             1.00000000 0.1005098 -0.01185387  0.34588146       -0.1019529
## Milk              0.10050977 1.0000000  0.72833512  0.12399376        0.6618157
## Grocery          -0.01185387 0.7283351  1.00000000 -0.04019274        0.9246407
## Frozen            0.34588146 0.1239938 -0.04019274  1.00000000       -0.1315249
## Detergents_Paper -0.10195294 0.6618157  0.92464069 -0.13152491        1.0000000
## Delicassen        0.24468997 0.4063683  0.20549651  0.39094747        0.0692913
##                  Delicassen
## Fresh             0.2446900
## Milk              0.4063683
## Grocery           0.2054965
## Frozen            0.3909475
## Detergents_Paper  0.0692913
## Delicassen        1.0000000
wholesale_data <- wholesale[,-c(1:2)]

# Using prcomp to compute the principal components (eigenvalues and eigenvectors). With scale=TRUE, variable means are set to zero, and variances set to one
wholesale_pca <- prcomp(wholesale_data,scale=TRUE)
wholesale_pca
## Standard deviations (1, .., p=5):
## [1] 1.6254958 1.1958226 0.7594873 0.5356839 0.2529693
## 
## Rotation (n x k) = (5 x 5):
##                          PC1        PC2         PC3         PC4         PC5
## Milk             -0.54363795  0.1146154  0.09014458 -0.82543534 -0.04302952
## Grocery          -0.58193330 -0.1556719 -0.12777739  0.30993371  0.72438520
## Frozen           -0.03962544  0.7024176 -0.70857828  0.04761674 -0.02624427
## Detergents_Paper -0.55369302 -0.2718776 -0.19028739  0.34173928 -0.68301653
## Delicassen       -0.24013597  0.6287461  0.66125216  0.32178331 -0.07883018
summary(wholesale_pca)
## Importance of components:
##                           PC1    PC2    PC3     PC4    PC5
## Standard deviation     1.6255 1.1958 0.7595 0.53568 0.2530
## Proportion of Variance 0.5284 0.2860 0.1154 0.05739 0.0128
## Cumulative Proportion  0.5284 0.8145 0.9298 0.98720 1.0000
# sample scores stored in sparrows_pca$x
# singular values (square roots of eigenvalues) stored in sparrow_pca$sdev
# loadings (eigenvectors) are stored in sparrows_pca$rotation
# variable means stored in sparrows_pca$center
# variable standard deviations stored in sparrows_pca$scale
# A table containing eigenvalues and %'s accounted, follows
# Eigenvalues are sdev^2


(eigen_wholesale <- wholesale_pca$sdev^2)
## [1] 2.64223659 1.42999181 0.57682096 0.28695719 0.06399345
names(eigen_wholesale) <- paste("PC",1:5,sep="")
eigen_wholesale
##        PC1        PC2        PC3        PC4        PC5 
## 2.64223659 1.42999181 0.57682096 0.28695719 0.06399345
sumlambdas <- sum(eigen_wholesale)
sumlambdas
## [1] 5
propvar <- eigen_wholesale/sumlambdas
propvar
##        PC1        PC2        PC3        PC4        PC5 
## 0.52844732 0.28599836 0.11536419 0.05739144 0.01279869
cumvar_wholesale <- cumsum(propvar)
cumvar_wholesale
##       PC1       PC2       PC3       PC4       PC5 
## 0.5284473 0.8144457 0.9298099 0.9872013 1.0000000
matlambdas <- rbind(eigen_wholesale,propvar,cumvar_wholesale)
rownames(matlambdas) <- c("Eigenvalues","Prop. variance","Cum. prop. variance")
round(matlambdas,3)
##                       PC1   PC2   PC3   PC4   PC5
## Eigenvalues         2.642 1.430 0.577 0.287 0.064
## Prop. variance      0.528 0.286 0.115 0.057 0.013
## Cum. prop. variance 0.528 0.814 0.930 0.987 1.000
summary(wholesale_pca)
## Importance of components:
##                           PC1    PC2    PC3     PC4    PC5
## Standard deviation     1.6255 1.1958 0.7595 0.53568 0.2530
## Proportion of Variance 0.5284 0.2860 0.1154 0.05739 0.0128
## Cumulative Proportion  0.5284 0.8145 0.9298 0.98720 1.0000
wholesale_pca$rotation
##                          PC1        PC2         PC3         PC4         PC5
## Milk             -0.54363795  0.1146154  0.09014458 -0.82543534 -0.04302952
## Grocery          -0.58193330 -0.1556719 -0.12777739  0.30993371  0.72438520
## Frozen           -0.03962544  0.7024176 -0.70857828  0.04761674 -0.02624427
## Detergents_Paper -0.55369302 -0.2718776 -0.19028739  0.34173928 -0.68301653
## Delicassen       -0.24013597  0.6287461  0.66125216  0.32178331 -0.07883018
print(wholesale_pca)
## Standard deviations (1, .., p=5):
## [1] 1.6254958 1.1958226 0.7594873 0.5356839 0.2529693
## 
## Rotation (n x k) = (5 x 5):
##                          PC1        PC2         PC3         PC4         PC5
## Milk             -0.54363795  0.1146154  0.09014458 -0.82543534 -0.04302952
## Grocery          -0.58193330 -0.1556719 -0.12777739  0.30993371  0.72438520
## Frozen           -0.03962544  0.7024176 -0.70857828  0.04761674 -0.02624427
## Detergents_Paper -0.55369302 -0.2718776 -0.19028739  0.34173928 -0.68301653
## Delicassen       -0.24013597  0.6287461  0.66125216  0.32178331 -0.07883018
## Sample scores stored in sparrow_pca$x
wholesale_pca$x
##                 PC1           PC2           PC3           PC4          PC5
##   [1,]  -0.19707283 -0.3770084356  0.4339928374 -5.086349e-01 -0.001854585
##   [2,]  -0.45313294 -0.1211597823  0.2609418663 -3.508749e-01  0.040946165
##   [3,]  -0.81180172  1.3273282020  1.5940953009  4.144155e-01 -0.301861199
##   [4,]   0.79342916  0.6658443374 -0.3359082992  2.853570e-01  0.057266232
##   [5,]  -0.11570147  1.0073354473  0.7846578714  3.653701e-01 -0.003812347
##   [6,]   0.14370629 -0.2180994333  0.4452745197 -4.774821e-01 -0.059000770
##   [7,]   0.32567049 -0.6325704892  0.1196417115  1.399425e-01 -0.054904769
##   [8,]  -0.15665440 -0.0331363080  0.4012580200  2.786108e-01  0.032831032
##   [9,]   0.48890741 -0.4938233270  0.2485820432 -1.502553e-02  0.081354092
##  [10,]  -1.62027497 -0.5048683883  0.1499964109  1.363545e-01  0.145687282
##  [11,]  -0.66758413 -0.0238881161 -0.3383420998  4.676957e-01 -0.071596678
##  [12,]   0.92597350 -0.3515756476  0.0822191593  1.100768e-01  0.137720104
##  [13,]  -0.92658585 -0.1074909163  0.7247966859 -4.006276e-01  0.084630659
##  [14,]  -0.82672223 -0.5293360636 -0.4619419906  3.523687e-01  0.011172418
##  [15,]  -0.80858534 -0.3934991730  0.4585439002 -7.316764e-02 -0.020590692
##  [16,]   0.93709140 -0.5308636604  0.2043574976  9.831297e-02  0.032723673
##  [17,]  -0.60479469 -0.6384278916  0.2404058097 -1.647392e-01  0.095547612
##  [18,]   0.33914993  0.5663431002  1.1904730227 -6.896284e-02 -0.095319576
##  [19,]  -0.29126066  0.2233895662  0.4970352941  1.829471e-01  0.135411974
##  [20,]   0.29954840 -0.6312712075  0.0644977021  2.521058e-01  0.228237979
##  [21,]   0.33682556 -0.0861339420  0.4875413015  3.768933e-02 -0.164582644
##  [22,]   1.09654804 -0.0043401285 -0.1497704508  7.141227e-02 -0.040058284
##  [23,]   0.26619036  1.5683970175 -0.2467060883  6.670989e-01 -0.283900004
##  [24,]  -4.58054505  3.8072871727  3.3396697767 -1.130469e+00  0.254755186
##  [25,]  -1.19755447  0.8003953225  0.9263685687  3.438610e-01  0.074691495
##  [26,]   0.15537156 -0.8250948908  0.0157524281  4.829123e-02 -0.122135167
##  [27,]   1.03266607  0.0159926101 -0.0590410608  1.074156e-01  0.037212525
##  [28,]   1.09811094 -0.4373483299  0.2574858397  5.881782e-02  0.095718884
##  [29,]  -3.14687957  0.1506165427  0.8514050232 -2.440491e-01  0.374539040
##  [30,]   0.88052223 -0.2960335906  0.2061557803  1.353125e-02 -0.101725549
##  [31,]  -0.05215116 -0.0007608697  0.5787210362  4.390835e-01  0.330576240
##  [32,]   0.69579690 -0.0888786625  0.1462865658 -2.131695e-01 -0.043052084
##  [33,]   0.98632753 -0.5302711469  0.2387360039  3.962267e-02 -0.032243165
##  [34,]   0.41807632  0.4822328908 -0.4532962679 -1.084847e-01  0.315119579
##  [35,]   1.02591988 -0.4642031406  0.2470086458 -8.541622e-02 -0.021926123
##  [36,]  -0.21643153 -0.7002955975 -0.0286492746  8.763578e-02  0.089179114
##  [37,]   0.24158323  0.6313110592  1.0201656795  2.740459e-01  0.025899292
##  [38,]  -0.97020398 -0.5543555171 -0.1693693299 -2.287695e-01 -0.173107471
##  [39,]  -1.62332525 -0.9046825507  0.0284863528 -6.876237e-01  0.072911071
##  [40,]   0.95272626  1.4991601790 -0.5480032712  3.916575e-01 -0.200711189
##  [41,]   0.08308879  2.0275377344  0.1721111919  4.933808e-01 -0.142283907
##  [42,]   0.25869103  0.1421617102  0.4567992931  3.539627e-01 -0.122343929
##  [43,]  -0.87588116 -1.0635936007 -0.1589398770  1.228399e-01  0.005470463
##  [44,]  -2.00255094 -1.2141592087 -0.4235084566  2.189990e-01  0.292958699
##  [45,]  -0.30164586 -0.8128614625 -0.0610496539 -1.224052e-01 -0.009380470
##  [46,]  -2.83141245  0.3536181366  0.8431308911 -6.720454e-01  0.210311577
##  [47,]  -1.90336183 -0.5432914831 -0.0554886874 -2.103213e-01  0.468640242
##  [48,]  -9.41725404  0.5414621846 -0.4271519661 -1.731283e+00  0.133925231
##  [49,]  -0.44041724 -0.5408300715  0.2274220164  1.858785e-01 -0.085748415
##  [50,]  -3.63590895 -0.9762339518 -0.4172346295 -3.493400e-01 -0.008648759
##  [51,]   0.91517116  0.4104644981  0.1479309633  2.485985e-01 -0.124280227
##  [52,]   0.47041131 -0.6176023581  0.1716656472 -9.969138e-02  0.179345625
##  [53,]   0.34153413 -0.4009520531  0.3295290114  6.842046e-02 -0.084407972
##  [54,]  -0.75096260 -0.7685290601 -0.0652044882 -3.819017e-01 -0.096389717
##  [55,]   1.02036283  0.0487333009  0.1823242891  7.034276e-02 -0.039970438
##  [56,]   0.48573185 -0.3152336743  0.2495333559  1.398177e-02 -0.067490936
##  [57,]  -4.63920836 -0.8901055110 -0.5298270393 -1.038605e+00 -0.819611828
##  [58,]  -0.95925425 -0.7378871248  0.2151100896 -1.012359e-01 -0.479576833
##  [59,]   1.08902399 -0.4058042205  0.2500262845 -1.164280e-01 -0.034073572
##  [60,]   0.02055344 -0.4281666899  0.4332603258  4.625049e-02 -0.005978029
##  [61,]   0.20266611 -0.8307229912  0.0488423661  2.140045e-01 -0.112791726
##  [62,]  -8.37149191 -1.5623789638 -1.1584129243 -1.933842e-01  0.319907948
##  [63,]  -0.04643766 -0.0064623816 -0.3126388497 -6.399385e-02 -0.270890553
##  [64,]  -1.44256223 -0.3881746020 -0.2539083496 -7.828486e-02 -0.117075631
##  [65,]   0.84129649  0.1089106750 -0.1116094122  2.036070e-01 -0.090476223
##  [66,]  -5.88216805 -2.0643796924 -0.7569200156  1.028312e+00 -0.240375986
##  [67,]   0.42975520 -0.8439903706  0.0033292780  3.019871e-01 -0.042364665
##  [68,]  -0.59711484 -0.6209401671 -0.0494590712  1.373610e-01  0.119889933
##  [69,]   0.22115034  0.9618614565  0.1144127302 -2.362520e-01 -0.069370103
##  [70,]   1.02170230 -0.4498752241  0.1528820924 -2.238458e-01 -0.120372633
##  [71,]   0.84070633  1.2369213016 -1.0142299556  1.233516e-01  0.019609630
##  [72,]  -1.73915275  2.8610779436  2.4170622052  2.526060e+00  0.464898413
##  [73,]   0.62067938  0.7050255622 -1.0362899361 -3.073257e-01 -0.169665352
##  [74,]   0.26682334  0.6376948170 -0.8755662868 -1.254282e-01  0.361266482
##  [75,]  -0.04638691 -0.1674522707  0.3416721379 -5.974311e-02  0.280263771
##  [76,]   1.20012549  0.2925598478 -0.1589521213  5.912953e-03 -0.158188044
##  [77,]   0.54017219  0.6274661824 -0.7126274387  3.926234e-03  0.235234832
##  [78,]  -2.77004981 -1.1857563171 -0.3572508458  4.752266e-01  0.244348076
##  [79,]   1.12399443 -0.2721741808 -0.0502825534 -2.452565e-02 -0.008690418
##  [80,]   0.65209963 -0.1635736239  0.4455307307  1.627898e-02 -0.063766052
##  [81,]   1.03868601 -0.4709420234  0.2485400502  9.200612e-02  0.019753232
##  [82,]  -1.10479248 -1.0377605203 -0.1519433582 -3.801156e-02 -0.183875803
##  [83,]  -0.56696336 -0.1897705085  0.5070899455 -1.672162e-01  0.108922971
##  [84,]   1.03054389 -0.1083993421  0.0575018685  1.189421e-02 -0.086393476
##  [85,]   0.39812160 -0.6286896384 -0.0790878932  6.345882e-02 -0.312116534
##  [86,] -12.68123458 -2.9055675082 -1.5301790149  1.109718e+00  0.766109027
##  [87,]  -8.39266413 -0.7648749958 -0.0254756094 -5.643262e+00 -0.986574914
##  [88,]  -0.92068706  3.3879831694  2.5748630597  1.493591e+00 -0.172326436
##  [89,]   1.01342557  0.7716998749 -1.2224864249  1.620546e-01  0.127114509
##  [90,]   0.44301966  0.5731766717  0.4416464506  1.520250e-01  0.111153688
##  [91,]   1.19321062 -0.0368736054 -0.1796662555  4.390303e-02 -0.016938275
##  [92,]   0.80614475  0.8926142932 -0.7902658775  9.552051e-03 -0.091570032
##  [93,]  -5.24057761 -0.1447202035  0.1233521218 -7.733263e-02 -0.687874557
##  [94,]   0.52578694  5.0971997130 -4.2280974876  3.562690e-01 -0.235963847
##  [95,]  -0.79761716 -0.7786843800  0.0650273452 -6.281708e-01 -0.038072173
##  [96,]   0.71560919 -0.4279470962  0.2866668376 -4.319073e-02  0.305115990
##  [97,]   0.24404605 -0.8238016100  0.0398452920  2.543221e-01 -0.058548989
##  [98,]   1.32938626 -0.4629908981  0.1364874089 -1.157487e-02 -0.068943918
##  [99,]   1.32246301 -0.4351711891  0.1309323486  1.898908e-02 -0.058179488
## [100,]   1.02727861  0.2983698332 -0.5129768013 -9.591612e-02 -0.037799311
## [101,]  -1.13082005  0.0296427973  0.0885664798  4.577611e-01 -0.473247863
## [102,]  -1.34423210 -0.4240373165  0.0836781087  1.010917e-02  0.047409545
## [103,]  -0.21246138 -0.1865573632 -0.0137137578  1.731627e-02 -0.260442905
## [104,]   0.06820127  2.4096180816 -1.9396808134  4.447883e-01  0.178855067
## [105,]   0.80468449 -0.3727619490  0.0956486645  3.469641e-02 -0.086245320
## [106,]   0.94469735 -0.1982170834  0.3856879072  1.704796e-01  0.133073495
## [107,]  -0.66901612 -0.6188300049  0.3127463650  3.184159e-01 -0.351635129
## [108,]  -1.47652662 -0.4917273047 -0.2096213973  1.042837e-01 -0.366056895
## [109,]  -0.04077613 -0.3953887590  0.4044253759 -4.101700e-01 -0.011842382
## [110,]  -1.70666698 -0.7445501815 -0.0743597119 -8.805089e-01  1.888181050
## [111,]   0.99983015  0.1048203863  0.2865328374  7.158538e-02 -0.063314112
## [112,]  -1.37687414 -0.6081606384  0.1224336064 -4.770345e-02  0.202325530
## [113,]   0.68923179  1.2798147189 -0.4339000015  1.794542e-01 -0.120975838
## [114,]   0.90109151  0.2079202525  0.1193587893  2.975898e-02 -0.126406650
## [115,]   1.05901888  0.0493188652  0.1474579566  1.006991e-01 -0.020229691
## [116,]   1.05586310 -0.1034380740 -0.0528084643  1.030625e-01  0.051592527
## [117,]   0.94497402 -0.3443957553  0.0458862013 -1.318167e-01  0.081944110
## [118,]   0.63888952 -0.1290378910  0.2358638727 -1.088179e-01  0.200165919
## [119,]   0.94868598  0.3684258484 -0.3442094906  3.215203e-02 -0.045101450
## [120,]   0.98250864  0.1114467083 -0.1886718345 -8.411286e-02 -0.027206760
## [121,]   0.96940760 -0.0240916571  0.1173633154  1.211556e-01  0.083059013
## [122,]   1.00153477 -0.1658860503 -0.0390138016 -2.630435e-01 -0.062843175
## [123,]   1.28120984 -0.1024026325  0.1511531050  8.324730e-02 -0.121160465
## [124,]  -0.18913115 -0.3203897860 -0.1106006465 -7.592123e-01  0.209858651
## [125,]   0.86596557  0.4226150095 -0.1163835099  1.589650e-01 -0.026966052
## [126,]   0.40917867  1.9108688107 -2.0407836107  1.442061e-01  0.194309814
## [127,]   1.01779186  0.6950263922 -0.8546792729 -1.292082e-02 -0.092424266
## [128,]  -0.30277111 -0.0382865069  0.6076499875  1.001440e-02  0.248558255
## [129,]   0.39288434 -0.5444758971  0.2361887980 -8.086403e-01 -0.013436955
## [130,]   1.02620109  0.0404906424  0.3923445875  1.777608e-01 -0.109445886
## [131,]   1.00675513  0.5407968338 -0.4618272530 -7.625720e-02 -0.177348616
## [132,]   1.30343896 -0.4607099296  0.2643065329 -3.356327e-02 -0.100342543
## [133,]   0.95838681 -0.4869393345  0.1881508451 -5.659957e-02 -0.072253726
## [134,]   1.18401500 -0.4471723939  0.2570614765 -3.016307e-02 -0.062315609
## [135,]   1.07458712 -0.3650636260  0.2546463208 -8.959202e-02  0.028826429
## [136,]   1.08937421 -0.3717038493  0.1205741859 -1.843713e-02  0.045760580
## [137,]  -0.11183011  0.3043792045 -0.1516516077 -3.557179e-01 -0.032810349
## [138,]   0.20888553 -0.5275345677  0.1124609346 -5.930183e-01  0.376046862
## [139,]   0.47286002  0.1412503836  0.9606664322  5.895386e-02  0.130678757
## [140,]   0.67212442 -0.2671718542  0.3297977543 -3.097939e-01  0.003832633
## [141,]   0.28796809  0.2251490753  0.4384379673  1.275042e-01  0.208626132
## [142,]  -0.02250288 -0.0922838655  0.6251372899 -1.162354e+00  0.168419794
## [143,]   0.34418432 -0.1711513228 -0.2189102391 -5.212920e-01  0.467973078
## [144,]   1.07654549  0.6940836506 -0.9243576757 -1.694764e-02 -0.137634393
## [145,]   0.93281684 -0.5228990290  0.2694356743 -3.070418e-01 -0.050356643
## [146,]  -3.18443785 -0.7438540221  0.4066323700  1.583661e+00  0.575108123
## [147,]   1.06717252 -0.3397410076  0.2201744068 -9.358929e-02  0.024377222
## [148,]   0.80824332 -0.3302172553  0.1391921066 -1.604844e-01 -0.090258890
## [149,]   1.22430136  0.0871948598 -0.2591661155  4.019766e-02 -0.136947866
## [150,]   1.05447741 -0.1543326372  0.4536170345  5.211853e-02 -0.043550579
## [151,]   1.04333128 -0.2288550227  0.3594012592 -2.596068e-02 -0.035171898
## [152,]   0.84943798 -0.1035340420  0.5836853316 -1.020722e-01 -0.054543391
## [153,]   1.02940017 -0.1547998275 -0.1923899590  2.856667e-03  0.058902303
## [154,]   0.39707127 -0.0168057926  0.5788233217 -7.640874e-01 -0.066660671
## [155,]   1.38885601 -0.5690528884  0.2314207961 -2.124517e-02 -0.091789299
## [156,]  -2.10534411 -0.8790908783  0.1196340531  4.951007e-01 -0.399152538
## [157,]  -0.94690511 -0.3674869252  0.5395080461  7.169925e-01 -0.048400289
## [158,]   0.99393880 -0.0635048487 -0.2020406424  4.515528e-02 -0.065786576
## [159,]  -0.28531006 -0.3541772263  0.2917156994  4.519864e-02 -0.031081093
## [160,]  -1.03017136 -1.0361993602 -0.1707735459  2.128945e-01 -0.193738153
## [161,]  -0.35485260 -0.3853783711  0.3230685951  5.594227e-01  0.157293084
## [162,]   1.14689210  0.0795306282  0.6088149730  1.928414e-01 -0.150608121
## [163,]   0.92036981 -0.1025116285 -0.0397713887 -1.145054e-02  0.113646494
## [164,]  -3.05168162 -1.1166208170 -0.7159845011  1.537208e-01 -0.135355954
## [165,]  -0.14994267 -0.3913717078 -0.2421719977 -2.766832e-01 -0.036986765
## [166,]  -1.80878413  0.0566334496 -0.2422449984  3.512095e-02  0.230965549
## [167,]  -0.54851470  0.0452361851  0.7101191669  3.068431e-01 -0.259912693
## [168,]   0.71052625 -0.4665092314  0.2733552116 -6.900412e-02 -0.132030137
## [169,]   1.24301618 -0.2889456013  0.1342404677 -9.451263e-03 -0.074195145
## [170,]   1.12716773 -0.0936776748  0.0446746742  8.243335e-02  0.015988183
## [171,]  -0.90926104 -0.8317067060 -0.1998028894 -3.331411e-03 -0.147138197
## [172,]  -3.27135965  0.4844985168  1.3117135113 -9.195516e-01 -0.175570118
## [173,]   0.20685284 -0.5580156466  0.2248068955 -1.338342e-01 -0.062418192
## [174,]  -1.58573375 -1.0507762119 -0.2920206050  5.614834e-01 -0.069519512
## [175,]   0.83240063  0.0296716850  0.1511531426  2.142830e-01  0.216354135
## [176,]  -0.53378209 -0.5059735509  0.4009604478 -1.696169e-02  0.110272790
## [177,]   0.23300367  0.4510780875 -0.8435857968 -3.784251e-01  0.091638181
## [178,]   0.34523774  0.2986179690  0.6309155013 -3.748515e-01  0.116635082
## [179,]   0.52247477 -0.3031257221  0.1815526848 -5.867474e-01  0.200947639
## [180,]   0.63766473  0.5699523520  0.1113244841 -1.763475e-01 -0.062042887
## [181,]   0.01290303 -0.0294551255  0.7374726259  1.485187e-02  0.263695260
## [182,]  -3.32956183  3.6298166964 -0.2769640395 -1.248901e+00  0.071987331
## [183,]  -0.68822721 -0.9146602969 -0.0990009318 -1.158184e-01 -0.344501680
## [184,]  -7.47744667 15.7336154455  6.4071500330  1.566581e+00 -0.390933851
## [185,]   1.00703448 -0.6486837093  0.1682726870  5.514838e-02  0.204836624
## [186,]   0.81312626 -0.1310929456  0.0426500561 -6.519887e-01 -0.078055731
## [187,]   1.11229463  0.0242439747 -0.1370615402  1.328789e-01 -0.213249552
## [188,]  -0.24041783  0.0940055884 -0.8447029159 -2.866790e-01  0.072035440
## [189,]  -0.72607631 -0.5535689471 -0.4026667470  6.842392e-02 -0.259887453
## [190,]  -0.78285913 -0.3648986302  0.4627545482 -4.376192e-01  0.080242773
## [191,]   0.74272114  0.5531106755 -0.7682232617 -5.684404e-01 -0.044045398
## [192,]   1.27769586 -0.4528908326  0.1150534175  1.173032e-02 -0.010051253
## [193,]   1.09693599 -0.4344151638  0.2381189714 -4.626280e-02  0.021607927
## [194,]  -0.81285702 -0.8912956579 -0.1963626901  7.383901e-01  0.597568986
## [195,]   1.00169591 -0.2619137189  0.3502776810  1.257535e-01  0.033380504
## [196,]   0.45245343  0.9280037294 -0.5185901798 -1.246246e-01  0.129445254
## [197,]   0.08628883  2.7568111298 -1.8229643830 -1.018957e-01 -0.059879885
## [198,]  -0.39085008 -0.3955405972  0.1964547248  1.120201e-02 -0.014723123
## [199,]   0.66997842 -0.0262749566 -0.1984931057  1.164929e-01  0.283969333
## [200,]   1.02565202 -0.4494088678  0.2308137614 -1.343236e-01 -0.022683101
## [201,]  -2.23900996 -0.5878260801 -0.7085900734  8.764202e-02  0.116989345
## [202,]  -2.99546346 -0.6844705504 -0.6063795435  4.206181e-01 -0.406247403
## [203,]  -0.68180673  1.6877976045  1.1111432584 -1.448361e-01  0.296475108
## [204,]   1.10109815 -0.5880892539  0.1182040110  4.898085e-02 -0.075060624
## [205,]   0.89280368 -0.1557704566  0.2918836756  2.145287e-01  0.247566809
## [206,]  -2.04834810 -1.0164029887 -0.2749671288  1.925170e-01  0.277801549
## [207,]   1.22289397 -0.4091923864  0.1658758384 -1.619192e-02 -0.086383217
## [208,]   0.02999763 -0.4562055716 -0.3960906986  7.069393e-02 -0.444580597
## [209,]   0.29338844 -0.3614455997 -0.0080606821  1.020401e-01 -0.194049088
## [210,]  -2.07821189 -1.0624050684 -0.2629478297  9.111398e-02 -0.702586793
## [211,]   0.95666185  0.1415798527  0.4661520779  8.654914e-02 -0.108537036
## [212,]  -5.65091274 -0.5719339518 -0.7387671291 -1.300213e-01 -0.126122041
## [213,]   1.01303835 -0.0291142686  0.4447647467  1.647516e-01 -0.039979160
## [214,]  -0.07733767 -0.3524530076  0.1631543516 -1.007511e-01 -0.224364938
## [215,]  -0.54162222 -0.6955489007 -0.0163762810  1.424171e-01 -0.152658315
## [216,]  -1.23239191 -0.2683704471  0.2912940521 -1.525642e-02  0.112285888
## [217,]  -3.65784251 -1.5024946145 -0.4451166133  3.442908e-01  0.657875917
## [218,]   1.03509689  0.0266087310  0.1292185239  4.633317e-02 -0.017602064
## [219,]  -1.19058168  0.6205930559  1.2442387713  7.184164e-01  0.142727311
## [220,]   1.25137280 -0.2392367905 -0.0817948446  2.619077e-02 -0.024885647
## [221,]   1.16786662 -0.1694031479  0.1501129365  2.960327e-02 -0.038677735
## [222,]  -0.30619270 -0.8089351138  0.0668910915 -1.868201e-01  0.063360480
## [223,]   1.02353682  0.5442296394 -0.7992298261  8.139072e-02  0.023241419
## [224,]   0.64173440  0.4433723400 -0.3296613548  1.340806e-01  0.105076655
## [225,]   1.19242546 -0.3378506721  0.2671314257  4.137322e-02 -0.022546599
## [226,]   0.74927539 -0.3702922405  0.2832530799 -9.813612e-02  0.063127379
## [227,]  -0.04166179 -0.1845337776  0.1953124055 -4.971583e-03  0.146592921
## [228,]   1.03747427 -0.1018997011  0.0652443951 -9.734645e-02 -0.063282394
## [229,]   0.74782120 -0.6691384055 -0.0398167843  3.062108e-01 -0.753030645
## [230,]   0.82806814  0.5910908116 -0.5551384969 -1.856014e-02 -0.089465542
## [231,]   0.25762310  1.0470755800 -0.5119581753 -1.145021e-01  0.051283570
## [232,]   0.14712185 -0.2486236341  0.1632538632 -9.088454e-01 -0.116555921
## [233,]   0.92806057 -0.3530682004  0.3031763812  2.615664e-02  0.114450635
## [234,]   0.77748264 -0.4430065220  0.1067856518 -4.316804e-01  0.059574527
## [235,]   0.67882658  0.5685557802  0.1896331714  1.585129e-01  0.034903691
## [236,]   0.58424690 -0.3544175668  0.1247594862 -5.103974e-01 -0.111243449
## [237,]   1.07019195 -0.2560573276 -0.0902724213  6.404733e-02  0.048960534
## [238,]   0.93984852  0.4097679695 -0.1117504327 -2.455267e-01 -0.140479637
## [239,]   1.29676093 -0.3771593082  0.1253457821 -1.504406e-02 -0.080820647
## [240,]   0.65211081  0.6117600861 -0.0475416452  1.822848e-01 -0.037125264
## [241,]   0.35751675  1.5650061126 -0.8886851108  2.372639e-01  0.233027565
## [242,]   0.96409594 -0.0619058462  0.1362730091  2.831163e-02 -0.022388607
## [243,]   1.02852505  0.0209240042 -0.2246841232  1.443754e-01 -0.002387319
## [244,]   0.42242573 -0.0883244925  0.6300559875  1.449717e-01 -0.041947263
## [245,]  -0.37409228 -0.2051916783  0.3552773511 -7.683646e-02  0.167212011
## [246,]  -1.17838892 -0.5677000690  0.3926909992  7.040641e-01 -0.434158944
## [247,]   0.99935781 -0.2027092622  0.1142067686 -1.174565e-01 -0.067239648
## [248,]   1.26979462 -0.1376011824  0.0892026613  5.425859e-02 -0.100974997
## [249,]   0.74868436 -0.3609679907  0.3041702147 -4.226251e-01 -0.047178655
## [250,]   0.81396957  0.3749872762 -0.6333171467 -2.174539e-01 -0.138534187
## [251,]   1.04468274 -0.1831538258  0.1467280904 -7.118688e-02 -0.037489850
## [252,]  -5.00768849  0.2866944486 -0.4530671996  4.696430e-01 -0.518324418
## [253,]   0.74545878  0.8487520877 -0.5316791722  2.080796e-01  0.131960206
## [254,]  -0.38605647 -0.3822564073  0.3596740591 -1.697875e-01  1.053331483
## [255,]  -0.70708219  0.9391578638  0.4174818883 -1.347493e+00 -0.181354924
## [256,]   1.18411490  0.0030724566 -0.1056092382  8.228318e-02 -0.039791764
## [257,]   0.63210547 -0.4617583277  0.2382291091 -3.355262e-01  0.201599925
## [258,]   0.60371331  0.1584360306 -0.4021340143  2.429649e-01 -0.537359370
## [259,]   0.51724649  1.0841565656  0.0813394709  3.147487e-02 -0.197104415
## [260,]   0.38236102 -0.0600224883 -0.0825430899 -1.448918e-01  0.252324354
## [261,]   0.77157492 -0.4143575173  0.3222401594 -3.760689e-01 -0.093166151
## [262,]   1.16886889  0.4671003805 -0.6890125078 -7.043557e-03 -0.075260316
## [263,]   1.08603962 -0.3224084602  0.2292812684 -5.347571e-03 -0.065522333
## [264,]   0.50559973 -0.1198310239 -0.4845642221  3.683120e-01 -0.046730481
## [265,]  -1.05801199 -0.7327306364  0.2015378961 -2.695094e-02  0.128243055
## [266,]  -1.65734964  1.7937030127 -0.3176590716 -1.632266e+00  0.531331804
## [267,]  -1.47739059 -0.1772552412  0.1448843315  2.739655e-01  0.750619450
## [268,]   0.72868453  0.7388604273  0.4633191765  4.314102e-01 -0.139527389
## [269,]  -1.21350291 -0.8331254104 -0.1733097803  2.719002e-01  0.427226378
## [270,]   1.23813362 -0.2040031259 -0.1028955543  5.837019e-02 -0.082046653
## [271,]   1.19514203  0.2171972169 -0.5560636672 -3.087829e-02 -0.091495871
## [272,]   0.78067858 -0.0285014779  0.4761824614 -3.323474e-01 -0.080771179
## [273,]   0.26602762 -0.2600598349  0.4141737602 -5.980265e-01  0.329535881
## [274,]   0.86878444  0.5324167641 -0.0225250867 -4.330202e-02 -0.111256960
## [275,]   0.97282972 -0.2621784812  0.3694564929  4.112342e-02 -0.114859043
## [276,]   1.22069804 -0.3548028456  0.2178276618 -1.359238e-01 -0.121674632
## [277,]   0.38108645  0.5359681743  0.1031818081  1.588676e-01  0.228136410
## [278,]   1.07846333  1.8653583443 -2.2187714566  1.341660e-01 -0.237361123
## [279,]   0.87750350  0.5586473422 -0.2976317207  3.982789e-02 -0.030181815
## [280,]  -0.22439955 -0.2780541521  0.2576621230  6.954580e-02  0.028826443
## [281,]   0.92072808 -0.1969571181  0.3540777128 -1.174575e-01  0.008145334
## [282,]   0.04172049 -0.0827385077  0.4799604369 -1.985353e-01 -0.063973268
## [283,]   0.56179348  0.5294798027 -0.3505102112 -3.311987e-02 -0.019932544
## [284,]   0.77559110  1.2246245312 -0.9328150131 -7.866405e-02 -0.107268673
## [285,]  -0.05666773  1.0332866463 -0.6082059064  3.097958e-01  0.613305200
## [286,]   1.07514112 -0.4990147752  0.0360851368  6.764338e-02  0.101806296
## [287,]   0.99534417 -0.3724699669 -0.0025361652 -1.141551e-01 -0.206668238
## [288,]   0.87483219  0.8238467598 -0.7660903317  6.233610e-02 -0.026198954
## [289,]   1.19971862 -0.4370617387  0.1507336728  2.377307e-02 -0.080498744
## [290,]   1.33657531 -0.3792644504  0.0403934684 -1.991985e-02 -0.078747463
## [291,]   0.83674885 -0.2326950986  0.4778908332  7.063094e-02 -0.094983491
## [292,]   0.85316130 -0.0776399639  0.0255349598 -1.724166e-01  0.065639153
## [293,]   0.69360374  0.1417127149 -0.1231390079 -7.944642e-03  0.043145957
## [294,]  -0.93965965 -0.6554126047  0.0144458692 -3.368204e-01 -0.092794885
## [295,]   0.59455930 -0.1573054188  0.4481372130  2.453625e-01  0.214344165
## [296,]   0.66171399 -0.6451195060  0.1053069563  1.281564e-01 -0.038034651
## [297,]   0.90049568 -0.0190226696 -0.0533317316  1.344791e-01  0.026534235
## [298,]   0.25180413 -0.5274174486 -0.0489267035  1.892655e-01 -0.140887343
## [299,]  -0.16562608 -0.5647513335  0.0893655028  2.460353e-01 -0.051401842
## [300,]   1.15462330 -0.5205877239  0.2356021757  9.127424e-05  0.001409648
## [301,]   0.06749116 -0.1726847894  0.4762957660 -8.485776e-02 -0.093726153
## [302,]  -1.87238584 -0.9062380384 -0.4427004461 -1.810361e-01  0.108661941
## [303,]  -0.36075328 -0.8370400050  0.0032583493  2.182948e-01 -0.296139923
## [304,]  -0.89344120 -1.2389830186 -0.3587903929  7.500908e-01 -0.514394929
## [305,]  -2.24170924 -0.9151722866  0.0047365098  1.077483e+00 -0.014103893
## [306,]  -0.57018410 -0.5842186912  0.0578018787 -8.680445e-01 -0.071166812
## [307,]  -1.88935546 -0.5541561209 -0.0993321247 -2.146956e-02  0.333094843
## [308,]   0.92559692 -0.2371239152  0.2679024918 -5.256295e-02  0.020162445
## [309,]   1.05503352 -0.4215247836  0.2968103229  5.963136e-02  0.065581698
## [310,]  -1.82444685 -0.4800857869  0.0137381216 -1.292307e+00 -0.197719739
## [311,]   0.91380091  1.4544571140 -1.3567395155  1.620224e-01 -0.067659925
## [312,]   0.64646544 -0.2336199078 -0.2728305098  5.699709e-02  0.444370877
## [313,]  -2.05651935 -1.5961639143 -0.8061189963  1.441392e+00 -1.124041662
## [314,]   1.10515579  0.0942827022 -0.3658363964  4.389359e-02  0.019092121
## [315,]   0.58629339 -0.2366852388  0.1994980699  2.435903e-01  0.306900770
## [316,]  -1.18632311  0.1134601388  0.8352376886 -6.227835e-01  0.062245747
## [317,]   1.04565960  0.0243938808  0.0831196910  4.934935e-02  0.003501565
## [318,]   0.55882703 -0.1724359049  0.4057778341  8.754597e-02  0.179102456
## [319,]   0.88204365 -0.3180530565 -0.0985570540 -1.318735e-01  0.041084475
## [320,]  -3.11235419 -0.6616337617  0.0320866751 -1.164397e+00 -0.730470849
## [321,]   0.88439078 -0.3152197306  0.3659850754 -2.408060e-01 -0.013520147
## [322,]   0.80386112 -0.0072506990  0.0513815263  1.045981e-01  0.204073016
## [323,]   0.92745036 -0.1201143087 -0.3393779899  1.744727e-01 -0.088752154
## [324,]   0.37271862 -0.5907448216  0.0313892316  4.454996e-01  0.516413252
## [325,]   0.85971976  0.0136909553  0.1573108564 -1.846572e-01  0.003240288
## [326,]  -1.78946833  9.4426161661 -7.3561656089 -1.262653e-01  0.172452266
## [327,]   1.05267151  0.0916580173 -0.0880866187  2.103203e-03 -0.098249788
## [328,]   1.17723864 -0.4219320559  0.2890068608  1.941328e-03 -0.008117440
## [329,]   0.81408444  0.8645867977 -0.5709617552  1.088298e-01  0.029775378
## [330,]   0.85138951  0.2466297340 -0.3962137780  1.314342e-01  0.121544020
## [331,]   0.81990469  0.1028458245 -0.0887119701  1.122326e-01  0.204217975
## [332,]  -2.55569469 -0.9119772593 -0.2422695809  1.565106e-02  0.445203963
## [333,]   0.81764691  0.3357835077  0.5424978555 -2.891576e-03 -0.118900424
## [334,]  -7.61379702 -3.4878261273 -1.8570054614  4.487063e+00 -0.492430881
## [335,]   0.73733540  1.8203153674 -0.6665945815  4.988941e-01 -0.104095182
## [336,]  -0.43016311 -0.2108130517  0.3183683323  1.198782e-01  0.026361034
## [337,]   1.12215088 -0.3190418064  0.3242381916 -4.171648e-02 -0.053885459
## [338,]   0.95236916  0.7486749232 -0.7833034255  1.236485e-01 -0.040856249
## [339,]   0.77302224  1.6893212630 -1.9971202384  3.868789e-01  0.331097800
## [340,]   0.67925139  1.1382025886 -0.7816151404  3.759789e-01  0.111049057
## [341,]  -0.44952190 -0.7286057941  0.1357307410  5.248944e-01 -0.468668348
## [342,]  -0.49874907 -0.3767392711  0.3492630012  3.240041e-01 -0.081203551
## [343,]  -0.03297929 -0.5029489774  0.3096893528  1.177555e-02 -0.379628062
## [344,]  -2.53250139 -1.5660071985 -0.8480530559  1.184938e+00 -0.359835221
## [345,]   1.13340753 -0.1952182547 -0.0133121117 -1.458200e-02 -0.026484205
## [346,]   0.22596844 -0.7694471361  0.0206476758  2.730768e-01 -0.041278788
## [347,]  -0.94277386 -0.4648303557 -0.2772970552  3.357660e-01  0.052682251
## [348,]  -0.52623469 -0.2992166497 -0.1906294560  5.170232e-02  0.090517992
## [349,]   0.89883641 -0.3013837867  0.1566870505 -4.785936e-02 -0.155021430
## [350,]  -2.40481023 -0.9960767917 -0.5310822389 -4.374715e-02 -0.394974382
## [351,]   1.08068712 -0.1237118941  0.1927739106  6.405186e-02 -0.016769761
## [352,]  -2.45061408 -0.5584735441  0.0419149034  8.628946e-01 -0.367013462
## [353,]   1.19422964 -0.4293999671  0.1558240037 -5.857045e-02 -0.012704664
## [354,]  -1.46109306 -1.0443346120 -0.0859166808  7.205129e-01  0.203389284
## [355,]   0.29654054  0.8630742744 -0.1383954212 -3.401633e-01 -0.240078342
## [356,]   1.19246382 -0.5482961618  0.2104436785 -7.319833e-03  0.017614488
## [357,]   1.30670647 -0.0029419227 -0.0920076981  6.454974e-02 -0.118117924
## [358,]  -0.84837304 -1.2653251323 -0.3054295861  1.059554e+00  0.619631964
## [359,]  -0.53430822  1.4509195863  0.4951650461 -1.488780e+00 -0.307004553
## [360,]   0.74548879 -0.3141877231  0.4084485713 -5.018286e-01 -0.030554517
## [361,]   0.95060230 -0.1063642743 -0.0303243494 -1.610490e-01 -0.059279836
## [362,]   1.24298882 -0.3289021623  0.1503307078  8.015338e-03 -0.078577675
## [363,]   1.04927604 -0.3656586146  0.3065814927 -2.120530e-02  0.028795306
## [364,]   0.87486904 -0.6155984555  0.1869141366  1.449102e-01  0.031142672
## [365,]   1.13722957 -0.3566829731  0.1603429922  3.141357e-02 -0.081879125
## [366,]  -0.34134077  0.0528651642  0.5204387607  2.484323e-01 -0.266636410
## [367,]   1.06478454 -0.3160073629  0.1713890889 -1.369749e-01 -0.037004496
## [368,]   1.23457189 -0.3020715155  0.1031540306 -3.290657e-02 -0.118323974
## [369,]   1.09202865 -0.1860571487  0.0523766298  1.397055e-02  0.035019264
## [370,]   1.29790056 -0.3646317914  0.1456950323  1.026699e-02 -0.070216959
## [371,]   0.54728205  0.0660108492  0.5275880023  4.670435e-03  0.109653457
## [372,]   0.92861428  0.7341864175 -0.7960212484  5.201769e-02 -0.132267223
## [373,]   0.55848361  0.6329891063  1.2548922421  1.947481e-01 -0.193946445
## [374,]  -0.01036762  0.1984867185  0.6528332213  2.705561e-02  0.057534446
## [375,]   1.02837629 -0.2211011595  0.1777392160 -1.044276e-01 -0.058081877
## [376,]   1.15932849 -0.5015726865  0.1543070714 -9.802522e-02 -0.093532531
## [377,]  -0.77356526  0.1996188872 -0.5105311814  8.662076e-03  0.146226030
## [378,]   0.88358086 -0.1532556029  0.3813297561 -1.293612e-01  0.029117565
## [379,]   0.93923945 -0.2746083703  0.4739350118 -1.933370e-01 -0.016908645
## [380,]   0.27600519 -0.6575609068  0.1558497541 -1.804023e-01  0.539501791
## [381,]   1.07810889 -0.0128717819 -0.3024832323  5.457804e-02 -0.056683715
## [382,]   0.81131596  1.0058196043 -1.0577260590 -3.067384e-01 -0.107566207
## [383,]  -0.12863861  0.3117748537  0.4582050708 -9.939952e-02  0.162220332
## [384,]   0.98212572  0.0222401601 -0.3036920467  4.719205e-02  0.066127080
## [385,]  -1.64808006  1.1586559064  0.9605663032 -1.324026e+00  0.742990749
## [386,]   1.10233193  0.0088755009  0.0972514015  8.876743e-02 -0.053949151
## [387,]   0.82259230 -0.0935972530  0.1765052575 -1.786855e-01  0.008277633
## [388,]   1.04129188 -0.0912372095  0.1742296693 -3.926493e-02 -0.062097721
## [389,]   1.19768522 -0.2641713568  0.0789849464 -1.220946e-03 -0.064952858
## [390,]   1.09437876 -0.0030619385 -0.0478148524 -2.252481e-02 -0.068766279
## [391,]   1.06891237  0.4179833336 -0.3424848203  7.987405e-02 -0.108186282
## [392,]   0.88438236 -0.0417631467  0.5367800244 -3.089990e-02 -0.009649391
## [393,]   0.79981986 -0.3397531358  0.2968846699 -2.819700e-01  0.110441519
## [394,]   0.48759544  0.8695421826 -0.8090023384 -4.435117e-01  0.028695796
## [395,]   1.07628493 -0.3243979663  0.1054144579  6.200560e-02  0.097367055
## [396,]   1.08292394 -0.1408151659 -0.1508761886 -5.685268e-03 -0.156053509
## [397,]  -0.65441107  0.1365619541  0.2609186633 -5.374683e-01 -0.017928094
## [398,]   1.06672699  0.5739678319 -0.5833083159 -5.032264e-03 -0.068046024
## [399,]   1.21812567  0.2573167088 -0.4850298560 -3.179681e-02 -0.108576616
## [400,]   1.20418087 -0.2977446541  0.0719496515  3.635687e-02 -0.118696408
## [401,]   1.12755720  0.1486469749 -0.0539299714  7.907698e-02 -0.080788486
## [402,]   0.78619937  1.7607701632 -1.2401567867  8.773626e-02 -0.092231125
## [403,]   0.70963764 -0.4824173163  0.2787551961 -3.455904e-01  0.247948235
## [404,]   0.21181784 -0.4378501159  0.3382349083 -1.023084e+00  0.087221718
## [405,]   0.65039342  0.1682494910 -0.2479710243 -2.358100e-01 -0.038949793
## [406,]   1.13695208 -0.2329491833  0.0020048404  5.289853e-03 -0.124123853
## [407,]   0.43799628  0.9861577681 -1.0141918729 -1.341328e-01  0.017341293
## [408,]  -1.67259278 -0.5997607604 -0.4539003847 -1.927750e-01  0.088799367
## [409,]   0.36550163 -0.4654167058 -0.0653570248  4.368427e-03 -0.044121872
## [410,]   0.05904374  0.7407264885  0.9812353376  5.321543e-01 -0.116912163
## [411,]   0.58114647 -0.1053616044  0.3728519656  2.555079e-01 -0.091531240
## [412,]   0.54871526  0.5993113197  1.0280690648  2.474061e-01 -0.033336374
## [413,]   0.02754893 -0.8683954018  0.0009452655  2.004207e-01  0.396172149
## [414,]   0.18022987  2.4627986053 -1.8610262286  1.696222e-01  0.081699407
## [415,]   0.84472130  0.2166544351 -0.5858918678  3.730761e-02 -0.052819470
## [416,]  -0.15011103 -0.1654789686  0.2521128931  6.515206e-02 -0.052293459
## [417,]  -0.94319868 -0.6282524920  0.0694434201 -2.856556e-01 -0.328750555
## [418,]  -0.17681577 -0.5846549679  0.2174968459  9.846607e-02  0.179411157
## [419,]  -1.21247875 -0.9451190928 -0.0111536007  2.085788e-01  0.281727286
## [420,]   0.67045226 -0.2169645295  0.4594481571 -7.930226e-02 -0.225166310
## [421,]  -0.70505273 -0.7893865579  0.1792825081  4.685864e-01 -0.138527213
## [422,]  -0.06490484 -0.3007384881  0.3109499418  1.898877e-01  0.016876618
## [423,]   0.82591686 -0.2892677213  0.3292781858  1.754135e-01  0.035366768
## [424,]   0.57180936 -0.3995984651  0.1544486982 -6.623976e-02 -0.049472294
## [425,]   0.04046836 -0.7367264203 -0.0847164943  3.219454e-01  0.343336774
## [426,]   0.76883248  2.0500342258 -1.5657601158  1.670196e-01 -0.067827419
## [427,]  -0.93848842 -0.0821362098 -0.0534415939  1.076078e-02  0.138959378
## [428,]  -0.43132555  2.0067711242 -1.5734003459 -1.398859e+00  0.039329073
## [429,]   0.51934102 -0.2273851246 -0.0315692426 -4.106207e-01  0.096672075
## [430,]   0.83217183 -0.0517546591  0.7913966759  1.911758e-01  0.080207639
## [431,]  -0.12732308 -0.2510251070  0.4661498794  3.030175e-01  1.035711609
## [432,]   0.28430937  1.6278170123 -1.4322862099 -6.732602e-02 -0.051096480
## [433,]   0.83664364 -0.5884685158  0.1925679473  1.462679e-01  0.052584928
## [434,]   0.89763536 -0.0286593561  0.3618008079 -1.269600e-01 -0.105069502
## [435,]   0.27267232 -0.4987640539  0.1838051451  7.266804e-02  0.119401988
## [436,]  -0.78171970  1.7262064236 -1.2339946527 -4.534560e-01  0.892440952
## [437,]   1.00383404  0.6000966110  0.1372499975  1.617472e-01 -0.153667550
## [438,]  -3.47543102 -1.2015869428 -0.1938524404  5.134742e-01 -0.065875377
## [439,]   0.91187529  0.0286815529  0.5761825595  9.421507e-02 -0.030771798
## [440,]   1.06427400 -0.6008476585  0.2126003922 -8.899895e-02  0.011009682
attach(wholesale)
# Identifying the scores by their Channel status
wholesale_channel_pca <- cbind(data.frame(Channel),wholesale_pca$x)
wholesale_channel_pca
##     Channel          PC1           PC2           PC3           PC4          PC5
## 1    Retail  -0.19707283 -0.3770084356  0.4339928374 -5.086349e-01 -0.001854585
## 2    Retail  -0.45313294 -0.1211597823  0.2609418663 -3.508749e-01  0.040946165
## 3    Retail  -0.81180172  1.3273282020  1.5940953009  4.144155e-01 -0.301861199
## 4    Horeca   0.79342916  0.6658443374 -0.3359082992  2.853570e-01  0.057266232
## 5    Retail  -0.11570147  1.0073354473  0.7846578714  3.653701e-01 -0.003812347
## 6    Retail   0.14370629 -0.2180994333  0.4452745197 -4.774821e-01 -0.059000770
## 7    Retail   0.32567049 -0.6325704892  0.1196417115  1.399425e-01 -0.054904769
## 8    Retail  -0.15665440 -0.0331363080  0.4012580200  2.786108e-01  0.032831032
## 9    Horeca   0.48890741 -0.4938233270  0.2485820432 -1.502553e-02  0.081354092
## 10   Retail  -1.62027497 -0.5048683883  0.1499964109  1.363545e-01  0.145687282
## 11   Retail  -0.66758413 -0.0238881161 -0.3383420998  4.676957e-01 -0.071596678
## 12   Retail   0.92597350 -0.3515756476  0.0822191593  1.100768e-01  0.137720104
## 13   Retail  -0.92658585 -0.1074909163  0.7247966859 -4.006276e-01  0.084630659
## 14   Retail  -0.82672223 -0.5293360636 -0.4619419906  3.523687e-01  0.011172418
## 15   Retail  -0.80858534 -0.3934991730  0.4585439002 -7.316764e-02 -0.020590692
## 16   Horeca   0.93709140 -0.5308636604  0.2043574976  9.831297e-02  0.032723673
## 17   Retail  -0.60479469 -0.6384278916  0.2404058097 -1.647392e-01  0.095547612
## 18   Horeca   0.33914993  0.5663431002  1.1904730227 -6.896284e-02 -0.095319576
## 19   Retail  -0.29126066  0.2233895662  0.4970352941  1.829471e-01  0.135411974
## 20   Horeca   0.29954840 -0.6312712075  0.0644977021  2.521058e-01  0.228237979
## 21   Retail   0.33682556 -0.0861339420  0.4875413015  3.768933e-02 -0.164582644
## 22   Horeca   1.09654804 -0.0043401285 -0.1497704508  7.141227e-02 -0.040058284
## 23   Horeca   0.26619036  1.5683970175 -0.2467060883  6.670989e-01 -0.283900004
## 24   Retail  -4.58054505  3.8072871727  3.3396697767 -1.130469e+00  0.254755186
## 25   Retail  -1.19755447  0.8003953225  0.9263685687  3.438610e-01  0.074691495
## 26   Retail   0.15537156 -0.8250948908  0.0157524281  4.829123e-02 -0.122135167
## 27   Horeca   1.03266607  0.0159926101 -0.0590410608  1.074156e-01  0.037212525
## 28   Horeca   1.09811094 -0.4373483299  0.2574858397  5.881782e-02  0.095718884
## 29   Retail  -3.14687957  0.1506165427  0.8514050232 -2.440491e-01  0.374539040
## 30   Horeca   0.88052223 -0.2960335906  0.2061557803  1.353125e-02 -0.101725549
## 31   Horeca  -0.05215116 -0.0007608697  0.5787210362  4.390835e-01  0.330576240
## 32   Horeca   0.69579690 -0.0888786625  0.1462865658 -2.131695e-01 -0.043052084
## 33   Horeca   0.98632753 -0.5302711469  0.2387360039  3.962267e-02 -0.032243165
## 34   Horeca   0.41807632  0.4822328908 -0.4532962679 -1.084847e-01  0.315119579
## 35   Horeca   1.02591988 -0.4642031406  0.2470086458 -8.541622e-02 -0.021926123
## 36   Retail  -0.21643153 -0.7002955975 -0.0286492746  8.763578e-02  0.089179114
## 37   Horeca   0.24158323  0.6313110592  1.0201656795  2.740459e-01  0.025899292
## 38   Retail  -0.97020398 -0.5543555171 -0.1693693299 -2.287695e-01 -0.173107471
## 39   Retail  -1.62332525 -0.9046825507  0.0284863528 -6.876237e-01  0.072911071
## 40   Horeca   0.95272626  1.4991601790 -0.5480032712  3.916575e-01 -0.200711189
## 41   Horeca   0.08308879  2.0275377344  0.1721111919  4.933808e-01 -0.142283907
## 42   Horeca   0.25869103  0.1421617102  0.4567992931  3.539627e-01 -0.122343929
## 43   Retail  -0.87588116 -1.0635936007 -0.1589398770  1.228399e-01  0.005470463
## 44   Retail  -2.00255094 -1.2141592087 -0.4235084566  2.189990e-01  0.292958699
## 45   Retail  -0.30164586 -0.8128614625 -0.0610496539 -1.224052e-01 -0.009380470
## 46   Retail  -2.83141245  0.3536181366  0.8431308911 -6.720454e-01  0.210311577
## 47   Retail  -1.90336183 -0.5432914831 -0.0554886874 -2.103213e-01  0.468640242
## 48   Retail  -9.41725404  0.5414621846 -0.4271519661 -1.731283e+00  0.133925231
## 49   Retail  -0.44041724 -0.5408300715  0.2274220164  1.858785e-01 -0.085748415
## 50   Retail  -3.63590895 -0.9762339518 -0.4172346295 -3.493400e-01 -0.008648759
## 51   Horeca   0.91517116  0.4104644981  0.1479309633  2.485985e-01 -0.124280227
## 52   Horeca   0.47041131 -0.6176023581  0.1716656472 -9.969138e-02  0.179345625
## 53   Retail   0.34153413 -0.4009520531  0.3295290114  6.842046e-02 -0.084407972
## 54   Retail  -0.75096260 -0.7685290601 -0.0652044882 -3.819017e-01 -0.096389717
## 55   Horeca   1.02036283  0.0487333009  0.1823242891  7.034276e-02 -0.039970438
## 56   Horeca   0.48573185 -0.3152336743  0.2495333559  1.398177e-02 -0.067490936
## 57   Retail  -4.63920836 -0.8901055110 -0.5298270393 -1.038605e+00 -0.819611828
## 58   Retail  -0.95925425 -0.7378871248  0.2151100896 -1.012359e-01 -0.479576833
## 59   Horeca   1.08902399 -0.4058042205  0.2500262845 -1.164280e-01 -0.034073572
## 60   Horeca   0.02055344 -0.4281666899  0.4332603258  4.625049e-02 -0.005978029
## 61   Retail   0.20266611 -0.8307229912  0.0488423661  2.140045e-01 -0.112791726
## 62   Retail  -8.37149191 -1.5623789638 -1.1584129243 -1.933842e-01  0.319907948
## 63   Retail  -0.04643766 -0.0064623816 -0.3126388497 -6.399385e-02 -0.270890553
## 64   Retail  -1.44256223 -0.3881746020 -0.2539083496 -7.828486e-02 -0.117075631
## 65   Horeca   0.84129649  0.1089106750 -0.1116094122  2.036070e-01 -0.090476223
## 66   Retail  -5.88216805 -2.0643796924 -0.7569200156  1.028312e+00 -0.240375986
## 67   Horeca   0.42975520 -0.8439903706  0.0033292780  3.019871e-01 -0.042364665
## 68   Retail  -0.59711484 -0.6209401671 -0.0494590712  1.373610e-01  0.119889933
## 69   Horeca   0.22115034  0.9618614565  0.1144127302 -2.362520e-01 -0.069370103
## 70   Horeca   1.02170230 -0.4498752241  0.1528820924 -2.238458e-01 -0.120372633
## 71   Horeca   0.84070633  1.2369213016 -1.0142299556  1.233516e-01  0.019609630
## 72   Horeca  -1.73915275  2.8610779436  2.4170622052  2.526060e+00  0.464898413
## 73   Horeca   0.62067938  0.7050255622 -1.0362899361 -3.073257e-01 -0.169665352
## 74   Retail   0.26682334  0.6376948170 -0.8755662868 -1.254282e-01  0.361266482
## 75   Retail  -0.04638691 -0.1674522707  0.3416721379 -5.974311e-02  0.280263771
## 76   Horeca   1.20012549  0.2925598478 -0.1589521213  5.912953e-03 -0.158188044
## 77   Horeca   0.54017219  0.6274661824 -0.7126274387  3.926234e-03  0.235234832
## 78   Retail  -2.77004981 -1.1857563171 -0.3572508458  4.752266e-01  0.244348076
## 79   Horeca   1.12399443 -0.2721741808 -0.0502825534 -2.452565e-02 -0.008690418
## 80   Horeca   0.65209963 -0.1635736239  0.4455307307  1.627898e-02 -0.063766052
## 81   Horeca   1.03868601 -0.4709420234  0.2485400502  9.200612e-02  0.019753232
## 82   Retail  -1.10479248 -1.0377605203 -0.1519433582 -3.801156e-02 -0.183875803
## 83   Retail  -0.56696336 -0.1897705085  0.5070899455 -1.672162e-01  0.108922971
## 84   Horeca   1.03054389 -0.1083993421  0.0575018685  1.189421e-02 -0.086393476
## 85   Retail   0.39812160 -0.6286896384 -0.0790878932  6.345882e-02 -0.312116534
## 86   Retail -12.68123458 -2.9055675082 -1.5301790149  1.109718e+00  0.766109027
## 87   Retail  -8.39266413 -0.7648749958 -0.0254756094 -5.643262e+00 -0.986574914
## 88   Horeca  -0.92068706  3.3879831694  2.5748630597  1.493591e+00 -0.172326436
## 89   Horeca   1.01342557  0.7716998749 -1.2224864249  1.620546e-01  0.127114509
## 90   Horeca   0.44301966  0.5731766717  0.4416464506  1.520250e-01  0.111153688
## 91   Horeca   1.19321062 -0.0368736054 -0.1796662555  4.390303e-02 -0.016938275
## 92   Horeca   0.80614475  0.8926142932 -0.7902658775  9.552051e-03 -0.091570032
## 93   Retail  -5.24057761 -0.1447202035  0.1233521218 -7.733263e-02 -0.687874557
## 94   Horeca   0.52578694  5.0971997130 -4.2280974876  3.562690e-01 -0.235963847
## 95   Retail  -0.79761716 -0.7786843800  0.0650273452 -6.281708e-01 -0.038072173
## 96   Horeca   0.71560919 -0.4279470962  0.2866668376 -4.319073e-02  0.305115990
## 97   Retail   0.24404605 -0.8238016100  0.0398452920  2.543221e-01 -0.058548989
## 98   Horeca   1.32938626 -0.4629908981  0.1364874089 -1.157487e-02 -0.068943918
## 99   Horeca   1.32246301 -0.4351711891  0.1309323486  1.898908e-02 -0.058179488
## 100  Horeca   1.02727861  0.2983698332 -0.5129768013 -9.591612e-02 -0.037799311
## 101  Retail  -1.13082005  0.0296427973  0.0885664798  4.577611e-01 -0.473247863
## 102  Retail  -1.34423210 -0.4240373165  0.0836781087  1.010917e-02  0.047409545
## 103  Retail  -0.21246138 -0.1865573632 -0.0137137578  1.731627e-02 -0.260442905
## 104  Horeca   0.06820127  2.4096180816 -1.9396808134  4.447883e-01  0.178855067
## 105  Horeca   0.80468449 -0.3727619490  0.0956486645  3.469641e-02 -0.086245320
## 106  Horeca   0.94469735 -0.1982170834  0.3856879072  1.704796e-01  0.133073495
## 107  Retail  -0.66901612 -0.6188300049  0.3127463650  3.184159e-01 -0.351635129
## 108  Retail  -1.47652662 -0.4917273047 -0.2096213973  1.042837e-01 -0.366056895
## 109  Retail  -0.04077613 -0.3953887590  0.4044253759 -4.101700e-01 -0.011842382
## 110  Retail  -1.70666698 -0.7445501815 -0.0743597119 -8.805089e-01  1.888181050
## 111  Horeca   0.99983015  0.1048203863  0.2865328374  7.158538e-02 -0.063314112
## 112  Retail  -1.37687414 -0.6081606384  0.1224336064 -4.770345e-02  0.202325530
## 113  Horeca   0.68923179  1.2798147189 -0.4339000015  1.794542e-01 -0.120975838
## 114  Horeca   0.90109151  0.2079202525  0.1193587893  2.975898e-02 -0.126406650
## 115  Horeca   1.05901888  0.0493188652  0.1474579566  1.006991e-01 -0.020229691
## 116  Horeca   1.05586310 -0.1034380740 -0.0528084643  1.030625e-01  0.051592527
## 117  Horeca   0.94497402 -0.3443957553  0.0458862013 -1.318167e-01  0.081944110
## 118  Horeca   0.63888952 -0.1290378910  0.2358638727 -1.088179e-01  0.200165919
## 119  Horeca   0.94868598  0.3684258484 -0.3442094906  3.215203e-02 -0.045101450
## 120  Horeca   0.98250864  0.1114467083 -0.1886718345 -8.411286e-02 -0.027206760
## 121  Horeca   0.96940760 -0.0240916571  0.1173633154  1.211556e-01  0.083059013
## 122  Horeca   1.00153477 -0.1658860503 -0.0390138016 -2.630435e-01 -0.062843175
## 123  Horeca   1.28120984 -0.1024026325  0.1511531050  8.324730e-02 -0.121160465
## 124  Retail  -0.18913115 -0.3203897860 -0.1106006465 -7.592123e-01  0.209858651
## 125  Horeca   0.86596557  0.4226150095 -0.1163835099  1.589650e-01 -0.026966052
## 126  Horeca   0.40917867  1.9108688107 -2.0407836107  1.442061e-01  0.194309814
## 127  Horeca   1.01779186  0.6950263922 -0.8546792729 -1.292082e-02 -0.092424266
## 128  Retail  -0.30277111 -0.0382865069  0.6076499875  1.001440e-02  0.248558255
## 129  Horeca   0.39288434 -0.5444758971  0.2361887980 -8.086403e-01 -0.013436955
## 130  Horeca   1.02620109  0.0404906424  0.3923445875  1.777608e-01 -0.109445886
## 131  Horeca   1.00675513  0.5407968338 -0.4618272530 -7.625720e-02 -0.177348616
## 132  Horeca   1.30343896 -0.4607099296  0.2643065329 -3.356327e-02 -0.100342543
## 133  Horeca   0.95838681 -0.4869393345  0.1881508451 -5.659957e-02 -0.072253726
## 134  Horeca   1.18401500 -0.4471723939  0.2570614765 -3.016307e-02 -0.062315609
## 135  Horeca   1.07458712 -0.3650636260  0.2546463208 -8.959202e-02  0.028826429
## 136  Horeca   1.08937421 -0.3717038493  0.1205741859 -1.843713e-02  0.045760580
## 137  Horeca  -0.11183011  0.3043792045 -0.1516516077 -3.557179e-01 -0.032810349
## 138  Horeca   0.20888553 -0.5275345677  0.1124609346 -5.930183e-01  0.376046862
## 139  Horeca   0.47286002  0.1412503836  0.9606664322  5.895386e-02  0.130678757
## 140  Horeca   0.67212442 -0.2671718542  0.3297977543 -3.097939e-01  0.003832633
## 141  Horeca   0.28796809  0.2251490753  0.4384379673  1.275042e-01  0.208626132
## 142  Horeca  -0.02250288 -0.0922838655  0.6251372899 -1.162354e+00  0.168419794
## 143  Horeca   0.34418432 -0.1711513228 -0.2189102391 -5.212920e-01  0.467973078
## 144  Horeca   1.07654549  0.6940836506 -0.9243576757 -1.694764e-02 -0.137634393
## 145  Horeca   0.93281684 -0.5228990290  0.2694356743 -3.070418e-01 -0.050356643
## 146  Retail  -3.18443785 -0.7438540221  0.4066323700  1.583661e+00  0.575108123
## 147  Horeca   1.06717252 -0.3397410076  0.2201744068 -9.358929e-02  0.024377222
## 148  Horeca   0.80824332 -0.3302172553  0.1391921066 -1.604844e-01 -0.090258890
## 149  Horeca   1.22430136  0.0871948598 -0.2591661155  4.019766e-02 -0.136947866
## 150  Horeca   1.05447741 -0.1543326372  0.4536170345  5.211853e-02 -0.043550579
## 151  Horeca   1.04333128 -0.2288550227  0.3594012592 -2.596068e-02 -0.035171898
## 152  Horeca   0.84943798 -0.1035340420  0.5836853316 -1.020722e-01 -0.054543391
## 153  Horeca   1.02940017 -0.1547998275 -0.1923899590  2.856667e-03  0.058902303
## 154  Horeca   0.39707127 -0.0168057926  0.5788233217 -7.640874e-01 -0.066660671
## 155  Horeca   1.38885601 -0.5690528884  0.2314207961 -2.124517e-02 -0.091789299
## 156  Retail  -2.10534411 -0.8790908783  0.1196340531  4.951007e-01 -0.399152538
## 157  Retail  -0.94690511 -0.3674869252  0.5395080461  7.169925e-01 -0.048400289
## 158  Horeca   0.99393880 -0.0635048487 -0.2020406424  4.515528e-02 -0.065786576
## 159  Retail  -0.28531006 -0.3541772263  0.2917156994  4.519864e-02 -0.031081093
## 160  Retail  -1.03017136 -1.0361993602 -0.1707735459  2.128945e-01 -0.193738153
## 161  Retail  -0.35485260 -0.3853783711  0.3230685951  5.594227e-01  0.157293084
## 162  Horeca   1.14689210  0.0795306282  0.6088149730  1.928414e-01 -0.150608121
## 163  Horeca   0.92036981 -0.1025116285 -0.0397713887 -1.145054e-02  0.113646494
## 164  Retail  -3.05168162 -1.1166208170 -0.7159845011  1.537208e-01 -0.135355954
## 165  Retail  -0.14994267 -0.3913717078 -0.2421719977 -2.766832e-01 -0.036986765
## 166  Retail  -1.80878413  0.0566334496 -0.2422449984  3.512095e-02  0.230965549
## 167  Retail  -0.54851470  0.0452361851  0.7101191669  3.068431e-01 -0.259912693
## 168  Horeca   0.71052625 -0.4665092314  0.2733552116 -6.900412e-02 -0.132030137
## 169  Horeca   1.24301618 -0.2889456013  0.1342404677 -9.451263e-03 -0.074195145
## 170  Horeca   1.12716773 -0.0936776748  0.0446746742  8.243335e-02  0.015988183
## 171  Retail  -0.90926104 -0.8317067060 -0.1998028894 -3.331411e-03 -0.147138197
## 172  Retail  -3.27135965  0.4844985168  1.3117135113 -9.195516e-01 -0.175570118
## 173  Horeca   0.20685284 -0.5580156466  0.2248068955 -1.338342e-01 -0.062418192
## 174  Retail  -1.58573375 -1.0507762119 -0.2920206050  5.614834e-01 -0.069519512
## 175  Horeca   0.83240063  0.0296716850  0.1511531426  2.142830e-01  0.216354135
## 176  Retail  -0.53378209 -0.5059735509  0.4009604478 -1.696169e-02  0.110272790
## 177  Horeca   0.23300367  0.4510780875 -0.8435857968 -3.784251e-01  0.091638181
## 178  Horeca   0.34523774  0.2986179690  0.6309155013 -3.748515e-01  0.116635082
## 179  Horeca   0.52247477 -0.3031257221  0.1815526848 -5.867474e-01  0.200947639
## 180  Horeca   0.63766473  0.5699523520  0.1113244841 -1.763475e-01 -0.062042887
## 181  Horeca   0.01290303 -0.0294551255  0.7374726259  1.485187e-02  0.263695260
## 182  Horeca  -3.32956183  3.6298166964 -0.2769640395 -1.248901e+00  0.071987331
## 183  Horeca  -0.68822721 -0.9146602969 -0.0990009318 -1.158184e-01 -0.344501680
## 184  Horeca  -7.47744667 15.7336154455  6.4071500330  1.566581e+00 -0.390933851
## 185  Horeca   1.00703448 -0.6486837093  0.1682726870  5.514838e-02  0.204836624
## 186  Horeca   0.81312626 -0.1310929456  0.0426500561 -6.519887e-01 -0.078055731
## 187  Horeca   1.11229463  0.0242439747 -0.1370615402  1.328789e-01 -0.213249552
## 188  Horeca  -0.24041783  0.0940055884 -0.8447029159 -2.866790e-01  0.072035440
## 189  Retail  -0.72607631 -0.5535689471 -0.4026667470  6.842392e-02 -0.259887453
## 190  Retail  -0.78285913 -0.3648986302  0.4627545482 -4.376192e-01  0.080242773
## 191  Horeca   0.74272114  0.5531106755 -0.7682232617 -5.684404e-01 -0.044045398
## 192  Horeca   1.27769586 -0.4528908326  0.1150534175  1.173032e-02 -0.010051253
## 193  Horeca   1.09693599 -0.4344151638  0.2381189714 -4.626280e-02  0.021607927
## 194  Retail  -0.81285702 -0.8912956579 -0.1963626901  7.383901e-01  0.597568986
## 195  Horeca   1.00169591 -0.2619137189  0.3502776810  1.257535e-01  0.033380504
## 196  Horeca   0.45245343  0.9280037294 -0.5185901798 -1.246246e-01  0.129445254
## 197  Horeca   0.08628883  2.7568111298 -1.8229643830 -1.018957e-01 -0.059879885
## 198  Retail  -0.39085008 -0.3955405972  0.1964547248  1.120201e-02 -0.014723123
## 199  Horeca   0.66997842 -0.0262749566 -0.1984931057  1.164929e-01  0.283969333
## 200  Horeca   1.02565202 -0.4494088678  0.2308137614 -1.343236e-01 -0.022683101
## 201  Retail  -2.23900996 -0.5878260801 -0.7085900734  8.764202e-02  0.116989345
## 202  Retail  -2.99546346 -0.6844705504 -0.6063795435  4.206181e-01 -0.406247403
## 203  Horeca  -0.68180673  1.6877976045  1.1111432584 -1.448361e-01  0.296475108
## 204  Horeca   1.10109815 -0.5880892539  0.1182040110  4.898085e-02 -0.075060624
## 205  Horeca   0.89280368 -0.1557704566  0.2918836756  2.145287e-01  0.247566809
## 206  Retail  -2.04834810 -1.0164029887 -0.2749671288  1.925170e-01  0.277801549
## 207  Horeca   1.22289397 -0.4091923864  0.1658758384 -1.619192e-02 -0.086383217
## 208  Retail   0.02999763 -0.4562055716 -0.3960906986  7.069393e-02 -0.444580597
## 209  Horeca   0.29338844 -0.3614455997 -0.0080606821  1.020401e-01 -0.194049088
## 210  Retail  -2.07821189 -1.0624050684 -0.2629478297  9.111398e-02 -0.702586793
## 211  Horeca   0.95666185  0.1415798527  0.4661520779  8.654914e-02 -0.108537036
## 212  Retail  -5.65091274 -0.5719339518 -0.7387671291 -1.300213e-01 -0.126122041
## 213  Horeca   1.01303835 -0.0291142686  0.4447647467  1.647516e-01 -0.039979160
## 214  Horeca  -0.07733767 -0.3524530076  0.1631543516 -1.007511e-01 -0.224364938
## 215  Retail  -0.54162222 -0.6955489007 -0.0163762810  1.424171e-01 -0.152658315
## 216  Horeca  -1.23239191 -0.2683704471  0.2912940521 -1.525642e-02  0.112285888
## 217  Retail  -3.65784251 -1.5024946145 -0.4451166133  3.442908e-01  0.657875917
## 218  Horeca   1.03509689  0.0266087310  0.1292185239  4.633317e-02 -0.017602064
## 219  Retail  -1.19058168  0.6205930559  1.2442387713  7.184164e-01  0.142727311
## 220  Horeca   1.25137280 -0.2392367905 -0.0817948446  2.619077e-02 -0.024885647
## 221  Horeca   1.16786662 -0.1694031479  0.1501129365  2.960327e-02 -0.038677735
## 222  Horeca  -0.30619270 -0.8089351138  0.0668910915 -1.868201e-01  0.063360480
## 223  Horeca   1.02353682  0.5442296394 -0.7992298261  8.139072e-02  0.023241419
## 224  Retail   0.64173440  0.4433723400 -0.3296613548  1.340806e-01  0.105076655
## 225  Horeca   1.19242546 -0.3378506721  0.2671314257  4.137322e-02 -0.022546599
## 226  Horeca   0.74927539 -0.3702922405  0.2832530799 -9.813612e-02  0.063127379
## 227  Retail  -0.04166179 -0.1845337776  0.1953124055 -4.971583e-03  0.146592921
## 228  Horeca   1.03747427 -0.1018997011  0.0652443951 -9.734645e-02 -0.063282394
## 229  Horeca   0.74782120 -0.6691384055 -0.0398167843  3.062108e-01 -0.753030645
## 230  Horeca   0.82806814  0.5910908116 -0.5551384969 -1.856014e-02 -0.089465542
## 231  Retail   0.25762310  1.0470755800 -0.5119581753 -1.145021e-01  0.051283570
## 232  Horeca   0.14712185 -0.2486236341  0.1632538632 -9.088454e-01 -0.116555921
## 233  Horeca   0.92806057 -0.3530682004  0.3031763812  2.615664e-02  0.114450635
## 234  Horeca   0.77748264 -0.4430065220  0.1067856518 -4.316804e-01  0.059574527
## 235  Horeca   0.67882658  0.5685557802  0.1896331714  1.585129e-01  0.034903691
## 236  Horeca   0.58424690 -0.3544175668  0.1247594862 -5.103974e-01 -0.111243449
## 237  Horeca   1.07019195 -0.2560573276 -0.0902724213  6.404733e-02  0.048960534
## 238  Horeca   0.93984852  0.4097679695 -0.1117504327 -2.455267e-01 -0.140479637
## 239  Horeca   1.29676093 -0.3771593082  0.1253457821 -1.504406e-02 -0.080820647
## 240  Horeca   0.65211081  0.6117600861 -0.0475416452  1.822848e-01 -0.037125264
## 241  Horeca   0.35751675  1.5650061126 -0.8886851108  2.372639e-01  0.233027565
## 242  Horeca   0.96409594 -0.0619058462  0.1362730091  2.831163e-02 -0.022388607
## 243  Horeca   1.02852505  0.0209240042 -0.2246841232  1.443754e-01 -0.002387319
## 244  Horeca   0.42242573 -0.0883244925  0.6300559875  1.449717e-01 -0.041947263
## 245  Horeca  -0.37409228 -0.2051916783  0.3552773511 -7.683646e-02  0.167212011
## 246  Retail  -1.17838892 -0.5677000690  0.3926909992  7.040641e-01 -0.434158944
## 247  Horeca   0.99935781 -0.2027092622  0.1142067686 -1.174565e-01 -0.067239648
## 248  Horeca   1.26979462 -0.1376011824  0.0892026613  5.425859e-02 -0.100974997
## 249  Horeca   0.74868436 -0.3609679907  0.3041702147 -4.226251e-01 -0.047178655
## 250  Horeca   0.81396957  0.3749872762 -0.6333171467 -2.174539e-01 -0.138534187
## 251  Horeca   1.04468274 -0.1831538258  0.1467280904 -7.118688e-02 -0.037489850
## 252  Retail  -5.00768849  0.2866944486 -0.4530671996  4.696430e-01 -0.518324418
## 253  Horeca   0.74545878  0.8487520877 -0.5316791722  2.080796e-01  0.131960206
## 254  Horeca  -0.38605647 -0.3822564073  0.3596740591 -1.697875e-01  1.053331483
## 255  Horeca  -0.70708219  0.9391578638  0.4174818883 -1.347493e+00 -0.181354924
## 256  Horeca   1.18411490  0.0030724566 -0.1056092382  8.228318e-02 -0.039791764
## 257  Horeca   0.63210547 -0.4617583277  0.2382291091 -3.355262e-01  0.201599925
## 258  Horeca   0.60371331  0.1584360306 -0.4021340143  2.429649e-01 -0.537359370
## 259  Horeca   0.51724649  1.0841565656  0.0813394709  3.147487e-02 -0.197104415
## 260  Horeca   0.38236102 -0.0600224883 -0.0825430899 -1.448918e-01  0.252324354
## 261  Horeca   0.77157492 -0.4143575173  0.3222401594 -3.760689e-01 -0.093166151
## 262  Horeca   1.16886889  0.4671003805 -0.6890125078 -7.043557e-03 -0.075260316
## 263  Horeca   1.08603962 -0.3224084602  0.2292812684 -5.347571e-03 -0.065522333
## 264  Horeca   0.50559973 -0.1198310239 -0.4845642221  3.683120e-01 -0.046730481
## 265  Retail  -1.05801199 -0.7327306364  0.2015378961 -2.695094e-02  0.128243055
## 266  Horeca  -1.65734964  1.7937030127 -0.3176590716 -1.632266e+00  0.531331804
## 267  Retail  -1.47739059 -0.1772552412  0.1448843315  2.739655e-01  0.750619450
## 268  Horeca   0.72868453  0.7388604273  0.4633191765  4.314102e-01 -0.139527389
## 269  Retail  -1.21350291 -0.8331254104 -0.1733097803  2.719002e-01  0.427226378
## 270  Horeca   1.23813362 -0.2040031259 -0.1028955543  5.837019e-02 -0.082046653
## 271  Horeca   1.19514203  0.2171972169 -0.5560636672 -3.087829e-02 -0.091495871
## 272  Horeca   0.78067858 -0.0285014779  0.4761824614 -3.323474e-01 -0.080771179
## 273  Horeca   0.26602762 -0.2600598349  0.4141737602 -5.980265e-01  0.329535881
## 274  Horeca   0.86878444  0.5324167641 -0.0225250867 -4.330202e-02 -0.111256960
## 275  Horeca   0.97282972 -0.2621784812  0.3694564929  4.112342e-02 -0.114859043
## 276  Horeca   1.22069804 -0.3548028456  0.2178276618 -1.359238e-01 -0.121674632
## 277  Horeca   0.38108645  0.5359681743  0.1031818081  1.588676e-01  0.228136410
## 278  Horeca   1.07846333  1.8653583443 -2.2187714566  1.341660e-01 -0.237361123
## 279  Horeca   0.87750350  0.5586473422 -0.2976317207  3.982789e-02 -0.030181815
## 280  Retail  -0.22439955 -0.2780541521  0.2576621230  6.954580e-02  0.028826443
## 281  Horeca   0.92072808 -0.1969571181  0.3540777128 -1.174575e-01  0.008145334
## 282  Retail   0.04172049 -0.0827385077  0.4799604369 -1.985353e-01 -0.063973268
## 283  Horeca   0.56179348  0.5294798027 -0.3505102112 -3.311987e-02 -0.019932544
## 284  Horeca   0.77559110  1.2246245312 -0.9328150131 -7.866405e-02 -0.107268673
## 285  Horeca  -0.05666773  1.0332866463 -0.6082059064  3.097958e-01  0.613305200
## 286  Horeca   1.07514112 -0.4990147752  0.0360851368  6.764338e-02  0.101806296
## 287  Horeca   0.99534417 -0.3724699669 -0.0025361652 -1.141551e-01 -0.206668238
## 288  Horeca   0.87483219  0.8238467598 -0.7660903317  6.233610e-02 -0.026198954
## 289  Horeca   1.19971862 -0.4370617387  0.1507336728  2.377307e-02 -0.080498744
## 290  Horeca   1.33657531 -0.3792644504  0.0403934684 -1.991985e-02 -0.078747463
## 291  Horeca   0.83674885 -0.2326950986  0.4778908332  7.063094e-02 -0.094983491
## 292  Horeca   0.85316130 -0.0776399639  0.0255349598 -1.724166e-01  0.065639153
## 293  Horeca   0.69360374  0.1417127149 -0.1231390079 -7.944642e-03  0.043145957
## 294  Retail  -0.93965965 -0.6554126047  0.0144458692 -3.368204e-01 -0.092794885
## 295  Horeca   0.59455930 -0.1573054188  0.4481372130  2.453625e-01  0.214344165
## 296  Retail   0.66171399 -0.6451195060  0.1053069563  1.281564e-01 -0.038034651
## 297  Horeca   0.90049568 -0.0190226696 -0.0533317316  1.344791e-01  0.026534235
## 298  Retail   0.25180413 -0.5274174486 -0.0489267035  1.892655e-01 -0.140887343
## 299  Retail  -0.16562608 -0.5647513335  0.0893655028  2.460353e-01 -0.051401842
## 300  Horeca   1.15462330 -0.5205877239  0.2356021757  9.127424e-05  0.001409648
## 301  Retail   0.06749116 -0.1726847894  0.4762957660 -8.485776e-02 -0.093726153
## 302  Retail  -1.87238584 -0.9062380384 -0.4427004461 -1.810361e-01  0.108661941
## 303  Retail  -0.36075328 -0.8370400050  0.0032583493  2.182948e-01 -0.296139923
## 304  Retail  -0.89344120 -1.2389830186 -0.3587903929  7.500908e-01 -0.514394929
## 305  Retail  -2.24170924 -0.9151722866  0.0047365098  1.077483e+00 -0.014103893
## 306  Retail  -0.57018410 -0.5842186912  0.0578018787 -8.680445e-01 -0.071166812
## 307  Retail  -1.88935546 -0.5541561209 -0.0993321247 -2.146956e-02  0.333094843
## 308  Horeca   0.92559692 -0.2371239152  0.2679024918 -5.256295e-02  0.020162445
## 309  Horeca   1.05503352 -0.4215247836  0.2968103229  5.963136e-02  0.065581698
## 310  Retail  -1.82444685 -0.4800857869  0.0137381216 -1.292307e+00 -0.197719739
## 311  Horeca   0.91380091  1.4544571140 -1.3567395155  1.620224e-01 -0.067659925
## 312  Horeca   0.64646544 -0.2336199078 -0.2728305098  5.699709e-02  0.444370877
## 313  Retail  -2.05651935 -1.5961639143 -0.8061189963  1.441392e+00 -1.124041662
## 314  Horeca   1.10515579  0.0942827022 -0.3658363964  4.389359e-02  0.019092121
## 315  Horeca   0.58629339 -0.2366852388  0.1994980699  2.435903e-01  0.306900770
## 316  Retail  -1.18632311  0.1134601388  0.8352376886 -6.227835e-01  0.062245747
## 317  Horeca   1.04565960  0.0243938808  0.0831196910  4.934935e-02  0.003501565
## 318  Horeca   0.55882703 -0.1724359049  0.4057778341  8.754597e-02  0.179102456
## 319  Horeca   0.88204365 -0.3180530565 -0.0985570540 -1.318735e-01  0.041084475
## 320  Retail  -3.11235419 -0.6616337617  0.0320866751 -1.164397e+00 -0.730470849
## 321  Horeca   0.88439078 -0.3152197306  0.3659850754 -2.408060e-01 -0.013520147
## 322  Horeca   0.80386112 -0.0072506990  0.0513815263  1.045981e-01  0.204073016
## 323  Horeca   0.92745036 -0.1201143087 -0.3393779899  1.744727e-01 -0.088752154
## 324  Horeca   0.37271862 -0.5907448216  0.0313892316  4.454996e-01  0.516413252
## 325  Horeca   0.85971976  0.0136909553  0.1573108564 -1.846572e-01  0.003240288
## 326  Horeca  -1.78946833  9.4426161661 -7.3561656089 -1.262653e-01  0.172452266
## 327  Horeca   1.05267151  0.0916580173 -0.0880866187  2.103203e-03 -0.098249788
## 328  Horeca   1.17723864 -0.4219320559  0.2890068608  1.941328e-03 -0.008117440
## 329  Horeca   0.81408444  0.8645867977 -0.5709617552  1.088298e-01  0.029775378
## 330  Horeca   0.85138951  0.2466297340 -0.3962137780  1.314342e-01  0.121544020
## 331  Horeca   0.81990469  0.1028458245 -0.0887119701  1.122326e-01  0.204217975
## 332  Retail  -2.55569469 -0.9119772593 -0.2422695809  1.565106e-02  0.445203963
## 333  Horeca   0.81764691  0.3357835077  0.5424978555 -2.891576e-03 -0.118900424
## 334  Retail  -7.61379702 -3.4878261273 -1.8570054614  4.487063e+00 -0.492430881
## 335  Retail   0.73733540  1.8203153674 -0.6665945815  4.988941e-01 -0.104095182
## 336  Retail  -0.43016311 -0.2108130517  0.3183683323  1.198782e-01  0.026361034
## 337  Horeca   1.12215088 -0.3190418064  0.3242381916 -4.171648e-02 -0.053885459
## 338  Horeca   0.95236916  0.7486749232 -0.7833034255  1.236485e-01 -0.040856249
## 339  Horeca   0.77302224  1.6893212630 -1.9971202384  3.868789e-01  0.331097800
## 340  Horeca   0.67925139  1.1382025886 -0.7816151404  3.759789e-01  0.111049057
## 341  Retail  -0.44952190 -0.7286057941  0.1357307410  5.248944e-01 -0.468668348
## 342  Retail  -0.49874907 -0.3767392711  0.3492630012  3.240041e-01 -0.081203551
## 343  Horeca  -0.03297929 -0.5029489774  0.3096893528  1.177555e-02 -0.379628062
## 344  Retail  -2.53250139 -1.5660071985 -0.8480530559  1.184938e+00 -0.359835221
## 345  Horeca   1.13340753 -0.1952182547 -0.0133121117 -1.458200e-02 -0.026484205
## 346  Horeca   0.22596844 -0.7694471361  0.0206476758  2.730768e-01 -0.041278788
## 347  Retail  -0.94277386 -0.4648303557 -0.2772970552  3.357660e-01  0.052682251
## 348  Retail  -0.52623469 -0.2992166497 -0.1906294560  5.170232e-02  0.090517992
## 349  Horeca   0.89883641 -0.3013837867  0.1566870505 -4.785936e-02 -0.155021430
## 350  Retail  -2.40481023 -0.9960767917 -0.5310822389 -4.374715e-02 -0.394974382
## 351  Horeca   1.08068712 -0.1237118941  0.1927739106  6.405186e-02 -0.016769761
## 352  Retail  -2.45061408 -0.5584735441  0.0419149034  8.628946e-01 -0.367013462
## 353  Horeca   1.19422964 -0.4293999671  0.1558240037 -5.857045e-02 -0.012704664
## 354  Retail  -1.46109306 -1.0443346120 -0.0859166808  7.205129e-01  0.203389284
## 355  Horeca   0.29654054  0.8630742744 -0.1383954212 -3.401633e-01 -0.240078342
## 356  Horeca   1.19246382 -0.5482961618  0.2104436785 -7.319833e-03  0.017614488
## 357  Horeca   1.30670647 -0.0029419227 -0.0920076981  6.454974e-02 -0.118117924
## 358  Retail  -0.84837304 -1.2653251323 -0.3054295861  1.059554e+00  0.619631964
## 359  Horeca  -0.53430822  1.4509195863  0.4951650461 -1.488780e+00 -0.307004553
## 360  Horeca   0.74548879 -0.3141877231  0.4084485713 -5.018286e-01 -0.030554517
## 361  Horeca   0.95060230 -0.1063642743 -0.0303243494 -1.610490e-01 -0.059279836
## 362  Horeca   1.24298882 -0.3289021623  0.1503307078  8.015338e-03 -0.078577675
## 363  Horeca   1.04927604 -0.3656586146  0.3065814927 -2.120530e-02  0.028795306
## 364  Horeca   0.87486904 -0.6155984555  0.1869141366  1.449102e-01  0.031142672
## 365  Horeca   1.13722957 -0.3566829731  0.1603429922  3.141357e-02 -0.081879125
## 366  Retail  -0.34134077  0.0528651642  0.5204387607  2.484323e-01 -0.266636410
## 367  Horeca   1.06478454 -0.3160073629  0.1713890889 -1.369749e-01 -0.037004496
## 368  Horeca   1.23457189 -0.3020715155  0.1031540306 -3.290657e-02 -0.118323974
## 369  Horeca   1.09202865 -0.1860571487  0.0523766298  1.397055e-02  0.035019264
## 370  Horeca   1.29790056 -0.3646317914  0.1456950323  1.026699e-02 -0.070216959
## 371  Retail   0.54728205  0.0660108492  0.5275880023  4.670435e-03  0.109653457
## 372  Horeca   0.92861428  0.7341864175 -0.7960212484  5.201769e-02 -0.132267223
## 373  Horeca   0.55848361  0.6329891063  1.2548922421  1.947481e-01 -0.193946445
## 374  Retail  -0.01036762  0.1984867185  0.6528332213  2.705561e-02  0.057534446
## 375  Horeca   1.02837629 -0.2211011595  0.1777392160 -1.044276e-01 -0.058081877
## 376  Horeca   1.15932849 -0.5015726865  0.1543070714 -9.802522e-02 -0.093532531
## 377  Retail  -0.77356526  0.1996188872 -0.5105311814  8.662076e-03  0.146226030
## 378  Horeca   0.88358086 -0.1532556029  0.3813297561 -1.293612e-01  0.029117565
## 379  Horeca   0.93923945 -0.2746083703  0.4739350118 -1.933370e-01 -0.016908645
## 380  Retail   0.27600519 -0.6575609068  0.1558497541 -1.804023e-01  0.539501791
## 381  Horeca   1.07810889 -0.0128717819 -0.3024832323  5.457804e-02 -0.056683715
## 382  Horeca   0.81131596  1.0058196043 -1.0577260590 -3.067384e-01 -0.107566207
## 383  Horeca  -0.12863861  0.3117748537  0.4582050708 -9.939952e-02  0.162220332
## 384  Horeca   0.98212572  0.0222401601 -0.3036920467  4.719205e-02  0.066127080
## 385  Horeca  -1.64808006  1.1586559064  0.9605663032 -1.324026e+00  0.742990749
## 386  Horeca   1.10233193  0.0088755009  0.0972514015  8.876743e-02 -0.053949151
## 387  Horeca   0.82259230 -0.0935972530  0.1765052575 -1.786855e-01  0.008277633
## 388  Horeca   1.04129188 -0.0912372095  0.1742296693 -3.926493e-02 -0.062097721
## 389  Horeca   1.19768522 -0.2641713568  0.0789849464 -1.220946e-03 -0.064952858
## 390  Horeca   1.09437876 -0.0030619385 -0.0478148524 -2.252481e-02 -0.068766279
## 391  Horeca   1.06891237  0.4179833336 -0.3424848203  7.987405e-02 -0.108186282
## 392  Horeca   0.88438236 -0.0417631467  0.5367800244 -3.089990e-02 -0.009649391
## 393  Horeca   0.79981986 -0.3397531358  0.2968846699 -2.819700e-01  0.110441519
## 394  Horeca   0.48759544  0.8695421826 -0.8090023384 -4.435117e-01  0.028695796
## 395  Horeca   1.07628493 -0.3243979663  0.1054144579  6.200560e-02  0.097367055
## 396  Horeca   1.08292394 -0.1408151659 -0.1508761886 -5.685268e-03 -0.156053509
## 397  Retail  -0.65441107  0.1365619541  0.2609186633 -5.374683e-01 -0.017928094
## 398  Horeca   1.06672699  0.5739678319 -0.5833083159 -5.032264e-03 -0.068046024
## 399  Horeca   1.21812567  0.2573167088 -0.4850298560 -3.179681e-02 -0.108576616
## 400  Horeca   1.20418087 -0.2977446541  0.0719496515  3.635687e-02 -0.118696408
## 401  Horeca   1.12755720  0.1486469749 -0.0539299714  7.907698e-02 -0.080788486
## 402  Horeca   0.78619937  1.7607701632 -1.2401567867  8.773626e-02 -0.092231125
## 403  Horeca   0.70963764 -0.4824173163  0.2787551961 -3.455904e-01  0.247948235
## 404  Horeca   0.21181784 -0.4378501159  0.3382349083 -1.023084e+00  0.087221718
## 405  Horeca   0.65039342  0.1682494910 -0.2479710243 -2.358100e-01 -0.038949793
## 406  Horeca   1.13695208 -0.2329491833  0.0020048404  5.289853e-03 -0.124123853
## 407  Horeca   0.43799628  0.9861577681 -1.0141918729 -1.341328e-01  0.017341293
## 408  Retail  -1.67259278 -0.5997607604 -0.4539003847 -1.927750e-01  0.088799367
## 409  Retail   0.36550163 -0.4654167058 -0.0653570248  4.368427e-03 -0.044121872
## 410  Horeca   0.05904374  0.7407264885  0.9812353376  5.321543e-01 -0.116912163
## 411  Horeca   0.58114647 -0.1053616044  0.3728519656  2.555079e-01 -0.091531240
## 412  Horeca   0.54871526  0.5993113197  1.0280690648  2.474061e-01 -0.033336374
## 413  Horeca   0.02754893 -0.8683954018  0.0009452655  2.004207e-01  0.396172149
## 414  Horeca   0.18022987  2.4627986053 -1.8610262286  1.696222e-01  0.081699407
## 415  Horeca   0.84472130  0.2166544351 -0.5858918678  3.730761e-02 -0.052819470
## 416  Retail  -0.15011103 -0.1654789686  0.2521128931  6.515206e-02 -0.052293459
## 417  Retail  -0.94319868 -0.6282524920  0.0694434201 -2.856556e-01 -0.328750555
## 418  Horeca  -0.17681577 -0.5846549679  0.2174968459  9.846607e-02  0.179411157
## 419  Retail  -1.21247875 -0.9451190928 -0.0111536007  2.085788e-01  0.281727286
## 420  Horeca   0.67045226 -0.2169645295  0.4594481571 -7.930226e-02 -0.225166310
## 421  Horeca  -0.70505273 -0.7893865579  0.1792825081  4.685864e-01 -0.138527213
## 422  Retail  -0.06490484 -0.3007384881  0.3109499418  1.898877e-01  0.016876618
## 423  Horeca   0.82591686 -0.2892677213  0.3292781858  1.754135e-01  0.035366768
## 424  Retail   0.57180936 -0.3995984651  0.1544486982 -6.623976e-02 -0.049472294
## 425  Retail   0.04046836 -0.7367264203 -0.0847164943  3.219454e-01  0.343336774
## 426  Horeca   0.76883248  2.0500342258 -1.5657601158  1.670196e-01 -0.067827419
## 427  Horeca  -0.93848842 -0.0821362098 -0.0534415939  1.076078e-02  0.138959378
## 428  Horeca  -0.43132555  2.0067711242 -1.5734003459 -1.398859e+00  0.039329073
## 429  Horeca   0.51934102 -0.2273851246 -0.0315692426 -4.106207e-01  0.096672075
## 430  Horeca   0.83217183 -0.0517546591  0.7913966759  1.911758e-01  0.080207639
## 431  Horeca  -0.12732308 -0.2510251070  0.4661498794  3.030175e-01  1.035711609
## 432  Horeca   0.28430937  1.6278170123 -1.4322862099 -6.732602e-02 -0.051096480
## 433  Horeca   0.83664364 -0.5884685158  0.1925679473  1.462679e-01  0.052584928
## 434  Horeca   0.89763536 -0.0286593561  0.3618008079 -1.269600e-01 -0.105069502
## 435  Horeca   0.27267232 -0.4987640539  0.1838051451  7.266804e-02  0.119401988
## 436  Horeca  -0.78171970  1.7262064236 -1.2339946527 -4.534560e-01  0.892440952
## 437  Horeca   1.00383404  0.6000966110  0.1372499975  1.617472e-01 -0.153667550
## 438  Retail  -3.47543102 -1.2015869428 -0.1938524404  5.134742e-01 -0.065875377
## 439  Horeca   0.91187529  0.0286815529  0.5761825595  9.421507e-02 -0.030771798
## 440  Horeca   1.06427400 -0.6008476585  0.2126003922 -8.899895e-02  0.011009682
# Means of scores for all the PC's classified by Channel status
tabmeansPC <- aggregate(wholesale_channel_pca[,2:6],by=list(Channel=wholesale$Channel),mean)
tabmeansPC
##   Channel        PC1        PC2         PC3         PC4          PC5
## 1  Horeca  0.6635514  0.2217411 -0.01580142 -0.02354574  0.008518129
## 2  Retail -1.3925234 -0.4653440  0.03316073  0.04941289 -0.017876074
tabmeansPC <- tabmeansPC[rev(order(tabmeansPC$Channel)),]
tabmeansPC
##   Channel        PC1        PC2         PC3         PC4          PC5
## 2  Retail -1.3925234 -0.4653440  0.03316073  0.04941289 -0.017876074
## 1  Horeca  0.6635514  0.2217411 -0.01580142 -0.02354574  0.008518129
tabfmeans <- t(tabmeansPC[,-1])
tabfmeans
##               2            1
## PC1 -1.39252342  0.663551430
## PC2 -0.46534399  0.221741094
## PC3  0.03316073 -0.015801420
## PC4  0.04941289 -0.023545742
## PC5 -0.01787607  0.008518129
colnames(tabfmeans) <- t(as.vector(tabmeansPC[1]$Channel))
tabfmeans
##          Retail       Horeca
## PC1 -1.39252342  0.663551430
## PC2 -0.46534399  0.221741094
## PC3  0.03316073 -0.015801420
## PC4  0.04941289 -0.023545742
## PC5 -0.01787607  0.008518129
# Standard deviations of scores for all the PC's classified by Channel status
tabsdsPC <- aggregate(wholesale_channel_pca[,2:6],by=list(Channel=wholesale$Channel),sd)
tabfsds <- t(tabsdsPC[,-1])
colnames(tabfsds) <- t(as.vector(tabsdsPC[1]$Channel))
tabfsds
##        Horeca    Retail
## PC1 0.7538240 2.0362088
## PC2 1.3036314 0.7419858
## PC3 0.8382756 0.5604593
## PC4 0.3619094 0.7835259
## PC5 0.1906575 0.3495700
t.test(PC1~wholesale$Channel,data=wholesale_channel_pca)
## 
##  Welch Two Sample t-test
## 
## data:  PC1 by wholesale$Channel
## t = 11.658, df = 159.69, p-value < 2.2e-16
## alternative hypothesis: true difference in means between group Horeca and group Retail is not equal to 0
## 95 percent confidence interval:
##  1.707764 2.404386
## sample estimates:
## mean in group Horeca mean in group Retail 
##            0.6635514           -1.3925234
t.test(PC2~wholesale$Channel,data=wholesale_channel_pca)
## 
##  Welch Two Sample t-test
## 
## data:  PC2 by wholesale$Channel
## t = 7.0199, df = 424.67, p-value = 8.846e-12
## alternative hypothesis: true difference in means between group Horeca and group Retail is not equal to 0
## 95 percent confidence interval:
##  0.4947011 0.8794690
## sample estimates:
## mean in group Horeca mean in group Retail 
##            0.2217411           -0.4653440
t.test(PC3~wholesale$Channel,data=wholesale_channel_pca)
## 
##  Welch Two Sample t-test
## 
## data:  PC3 by wholesale$Channel
## t = -0.72426, df = 390.94, p-value = 0.4693
## alternative hypothesis: true difference in means between group Horeca and group Retail is not equal to 0
## 95 percent confidence interval:
##  -0.18187283  0.08394853
## sample estimates:
## mean in group Horeca mean in group Retail 
##          -0.01580142           0.03316073
t.test(PC4~wholesale$Channel,data=wholesale_channel_pca)
## 
##  Welch Two Sample t-test
## 
## data:  PC4 by wholesale$Channel
## t = -1.0572, df = 170.29, p-value = 0.2919
## alternative hypothesis: true difference in means between group Horeca and group Retail is not equal to 0
## 95 percent confidence interval:
##  -0.20919064  0.06327337
## sample estimates:
## mean in group Horeca mean in group Retail 
##          -0.02354574           0.04941289
t.test(PC5~wholesale$Channel,data=wholesale_channel_pca)
## 
##  Welch Two Sample t-test
## 
## data:  PC5 by wholesale$Channel
## t = 0.84204, df = 182.07, p-value = 0.4009
## alternative hypothesis: true difference in means between group Horeca and group Retail is not equal to 0
## 95 percent confidence interval:
##  -0.0354529  0.0882413
## sample estimates:
## mean in group Horeca mean in group Retail 
##          0.008518129         -0.017876074
## F ratio tests
var.test(PC1~wholesale$Channel,data=wholesale_channel_pca)
## 
##  F test to compare two variances
## 
## data:  PC1 by wholesale$Channel
## F = 0.13706, num df = 297, denom df = 141, p-value < 2.2e-16
## alternative hypothesis: true ratio of variances is not equal to 1
## 95 percent confidence interval:
##  0.1023803 0.1808180
## sample estimates:
## ratio of variances 
##          0.1370551
var.test(PC2~wholesale$Channel,data=wholesale_channel_pca)
## 
##  F test to compare two variances
## 
## data:  PC2 by wholesale$Channel
## F = 3.0869, num df = 297, denom df = 141, p-value = 8.931e-13
## alternative hypothesis: true ratio of variances is not equal to 1
## 95 percent confidence interval:
##  2.305895 4.072535
## sample estimates:
## ratio of variances 
##           3.086871
var.test(PC3~wholesale$Channel,data=wholesale_channel_pca)
## 
##  F test to compare two variances
## 
## data:  PC3 by wholesale$Channel
## F = 2.2371, num df = 297, denom df = 141, p-value = 1.637e-07
## alternative hypothesis: true ratio of variances is not equal to 1
## 95 percent confidence interval:
##  1.671116 2.951425
## sample estimates:
## ratio of variances 
##             2.2371
var.test(PC4~wholesale$Channel,data=wholesale_channel_pca)
## 
##  F test to compare two variances
## 
## data:  PC4 by wholesale$Channel
## F = 0.21335, num df = 297, denom df = 141, p-value < 2.2e-16
## alternative hypothesis: true ratio of variances is not equal to 1
## 95 percent confidence interval:
##  0.1593728 0.2814747
## sample estimates:
## ratio of variances 
##          0.2133502
var.test(PC5~wholesale$Channel,data=wholesale_channel_pca)
## 
##  F test to compare two variances
## 
## data:  PC5 by wholesale$Channel
## F = 0.29747, num df = 297, denom df = 141, p-value < 2.2e-16
## alternative hypothesis: true ratio of variances is not equal to 1
## 95 percent confidence interval:
##  0.2222084 0.3924513
## sample estimates:
## ratio of variances 
##          0.2974675
# Levene's tests (one-sided)
library(car)
(LTPC1 <- leveneTest(PC1~wholesale$Channel,data=wholesale_channel_pca))
## Warning in leveneTest.default(y = y, group = group, ...): group coerced to
## factor.
## Levene's Test for Homogeneity of Variance (center = median)
##        Df F value  Pr(>F)    
## group   1  52.142 2.3e-12 ***
##       438                    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(p_PC1_1sided <- LTPC1[[3]][1]/2)
## [1] 1.150248e-12
(LTPC2 <- leveneTest(PC2~wholesale$Channel,data=wholesale_channel_pca))
## Warning in leveneTest.default(y = y, group = group, ...): group coerced to
## factor.
## Levene's Test for Homogeneity of Variance (center = median)
##        Df F value Pr(>F)
## group   1  1.0541 0.3051
##       438
(p_PC2_1sided=LTPC2[[3]][1]/2)
## [1] 0.152567
(LTPC3 <- leveneTest(PC3~wholesale$Channel,data=wholesale_channel_pca))
## Warning in leveneTest.default(y = y, group = group, ...): group coerced to
## factor.
## Levene's Test for Homogeneity of Variance (center = median)
##        Df F value Pr(>F)
## group   1  0.5024 0.4788
##       438
(p_PC3_1sided <- LTPC3[[3]][1]/2)
## [1] 0.2394059
(LTPC4 <- leveneTest(PC4~wholesale$Channel,data=wholesale_channel_pca))
## Warning in leveneTest.default(y = y, group = group, ...): group coerced to
## factor.
## Levene's Test for Homogeneity of Variance (center = median)
##        Df F value    Pr(>F)    
## group   1   20.69 7.001e-06 ***
##       438                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(p_PC4_1sided <- LTPC4[[3]][1]/2)
## [1] 3.500348e-06
(LTPC5 <- leveneTest(PC5~wholesale$Channel,data=wholesale_channel_pca))
## Warning in leveneTest.default(y = y, group = group, ...): group coerced to
## factor.
## Levene's Test for Homogeneity of Variance (center = median)
##        Df F value    Pr(>F)    
## group   1  34.481 8.517e-09 ***
##       438                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(p_PC5_1sided <- LTPC5[[3]][1]/2)
## [1] 4.258356e-09
# Plotting the scores for the first and second components
plot(wholesale_channel_pca$PC1, wholesale_channel_pca$PC2,pch=ifelse(wholesale_pca$Channel == "Retail",1,16),xlab="PC1", ylab="PC2", main="Wholesale Customers against PC1&PC2")
abline(h=0)
abline(v=0)
legend("bottomleft", legend=c("Retail","Horesca"), pch=c(1,16))

plot(eigen_wholesale, xlab = "Component number", ylab = "Component variance", type = "l", main = "Scree diagram")

plot(log(eigen_wholesale), xlab = "Component number",ylab = "log(Component variance)", type="l",main = "Log(eigenvalue) diagram")

print(summary(wholesale_pca))
## Importance of components:
##                           PC1    PC2    PC3     PC4    PC5
## Standard deviation     1.6255 1.1958 0.7595 0.53568 0.2530
## Proportion of Variance 0.5284 0.2860 0.1154 0.05739 0.0128
## Cumulative Proportion  0.5284 0.8145 0.9298 0.98720 1.0000
diag(cov(wholesale_pca$x))
##        PC1        PC2        PC3        PC4        PC5 
## 2.64223659 1.42999181 0.57682096 0.28695719 0.06399345
xlim <- range(wholesale_pca$x[,1])
wholesale_pca$x[,1]
##   [1]  -0.19707283  -0.45313294  -0.81180172   0.79342916  -0.11570147
##   [6]   0.14370629   0.32567049  -0.15665440   0.48890741  -1.62027497
##  [11]  -0.66758413   0.92597350  -0.92658585  -0.82672223  -0.80858534
##  [16]   0.93709140  -0.60479469   0.33914993  -0.29126066   0.29954840
##  [21]   0.33682556   1.09654804   0.26619036  -4.58054505  -1.19755447
##  [26]   0.15537156   1.03266607   1.09811094  -3.14687957   0.88052223
##  [31]  -0.05215116   0.69579690   0.98632753   0.41807632   1.02591988
##  [36]  -0.21643153   0.24158323  -0.97020398  -1.62332525   0.95272626
##  [41]   0.08308879   0.25869103  -0.87588116  -2.00255094  -0.30164586
##  [46]  -2.83141245  -1.90336183  -9.41725404  -0.44041724  -3.63590895
##  [51]   0.91517116   0.47041131   0.34153413  -0.75096260   1.02036283
##  [56]   0.48573185  -4.63920836  -0.95925425   1.08902399   0.02055344
##  [61]   0.20266611  -8.37149191  -0.04643766  -1.44256223   0.84129649
##  [66]  -5.88216805   0.42975520  -0.59711484   0.22115034   1.02170230
##  [71]   0.84070633  -1.73915275   0.62067938   0.26682334  -0.04638691
##  [76]   1.20012549   0.54017219  -2.77004981   1.12399443   0.65209963
##  [81]   1.03868601  -1.10479248  -0.56696336   1.03054389   0.39812160
##  [86] -12.68123458  -8.39266413  -0.92068706   1.01342557   0.44301966
##  [91]   1.19321062   0.80614475  -5.24057761   0.52578694  -0.79761716
##  [96]   0.71560919   0.24404605   1.32938626   1.32246301   1.02727861
## [101]  -1.13082005  -1.34423210  -0.21246138   0.06820127   0.80468449
## [106]   0.94469735  -0.66901612  -1.47652662  -0.04077613  -1.70666698
## [111]   0.99983015  -1.37687414   0.68923179   0.90109151   1.05901888
## [116]   1.05586310   0.94497402   0.63888952   0.94868598   0.98250864
## [121]   0.96940760   1.00153477   1.28120984  -0.18913115   0.86596557
## [126]   0.40917867   1.01779186  -0.30277111   0.39288434   1.02620109
## [131]   1.00675513   1.30343896   0.95838681   1.18401500   1.07458712
## [136]   1.08937421  -0.11183011   0.20888553   0.47286002   0.67212442
## [141]   0.28796809  -0.02250288   0.34418432   1.07654549   0.93281684
## [146]  -3.18443785   1.06717252   0.80824332   1.22430136   1.05447741
## [151]   1.04333128   0.84943798   1.02940017   0.39707127   1.38885601
## [156]  -2.10534411  -0.94690511   0.99393880  -0.28531006  -1.03017136
## [161]  -0.35485260   1.14689210   0.92036981  -3.05168162  -0.14994267
## [166]  -1.80878413  -0.54851470   0.71052625   1.24301618   1.12716773
## [171]  -0.90926104  -3.27135965   0.20685284  -1.58573375   0.83240063
## [176]  -0.53378209   0.23300367   0.34523774   0.52247477   0.63766473
## [181]   0.01290303  -3.32956183  -0.68822721  -7.47744667   1.00703448
## [186]   0.81312626   1.11229463  -0.24041783  -0.72607631  -0.78285913
## [191]   0.74272114   1.27769586   1.09693599  -0.81285702   1.00169591
## [196]   0.45245343   0.08628883  -0.39085008   0.66997842   1.02565202
## [201]  -2.23900996  -2.99546346  -0.68180673   1.10109815   0.89280368
## [206]  -2.04834810   1.22289397   0.02999763   0.29338844  -2.07821189
## [211]   0.95666185  -5.65091274   1.01303835  -0.07733767  -0.54162222
## [216]  -1.23239191  -3.65784251   1.03509689  -1.19058168   1.25137280
## [221]   1.16786662  -0.30619270   1.02353682   0.64173440   1.19242546
## [226]   0.74927539  -0.04166179   1.03747427   0.74782120   0.82806814
## [231]   0.25762310   0.14712185   0.92806057   0.77748264   0.67882658
## [236]   0.58424690   1.07019195   0.93984852   1.29676093   0.65211081
## [241]   0.35751675   0.96409594   1.02852505   0.42242573  -0.37409228
## [246]  -1.17838892   0.99935781   1.26979462   0.74868436   0.81396957
## [251]   1.04468274  -5.00768849   0.74545878  -0.38605647  -0.70708219
## [256]   1.18411490   0.63210547   0.60371331   0.51724649   0.38236102
## [261]   0.77157492   1.16886889   1.08603962   0.50559973  -1.05801199
## [266]  -1.65734964  -1.47739059   0.72868453  -1.21350291   1.23813362
## [271]   1.19514203   0.78067858   0.26602762   0.86878444   0.97282972
## [276]   1.22069804   0.38108645   1.07846333   0.87750350  -0.22439955
## [281]   0.92072808   0.04172049   0.56179348   0.77559110  -0.05666773
## [286]   1.07514112   0.99534417   0.87483219   1.19971862   1.33657531
## [291]   0.83674885   0.85316130   0.69360374  -0.93965965   0.59455930
## [296]   0.66171399   0.90049568   0.25180413  -0.16562608   1.15462330
## [301]   0.06749116  -1.87238584  -0.36075328  -0.89344120  -2.24170924
## [306]  -0.57018410  -1.88935546   0.92559692   1.05503352  -1.82444685
## [311]   0.91380091   0.64646544  -2.05651935   1.10515579   0.58629339
## [316]  -1.18632311   1.04565960   0.55882703   0.88204365  -3.11235419
## [321]   0.88439078   0.80386112   0.92745036   0.37271862   0.85971976
## [326]  -1.78946833   1.05267151   1.17723864   0.81408444   0.85138951
## [331]   0.81990469  -2.55569469   0.81764691  -7.61379702   0.73733540
## [336]  -0.43016311   1.12215088   0.95236916   0.77302224   0.67925139
## [341]  -0.44952190  -0.49874907  -0.03297929  -2.53250139   1.13340753
## [346]   0.22596844  -0.94277386  -0.52623469   0.89883641  -2.40481023
## [351]   1.08068712  -2.45061408   1.19422964  -1.46109306   0.29654054
## [356]   1.19246382   1.30670647  -0.84837304  -0.53430822   0.74548879
## [361]   0.95060230   1.24298882   1.04927604   0.87486904   1.13722957
## [366]  -0.34134077   1.06478454   1.23457189   1.09202865   1.29790056
## [371]   0.54728205   0.92861428   0.55848361  -0.01036762   1.02837629
## [376]   1.15932849  -0.77356526   0.88358086   0.93923945   0.27600519
## [381]   1.07810889   0.81131596  -0.12863861   0.98212572  -1.64808006
## [386]   1.10233193   0.82259230   1.04129188   1.19768522   1.09437876
## [391]   1.06891237   0.88438236   0.79981986   0.48759544   1.07628493
## [396]   1.08292394  -0.65441107   1.06672699   1.21812567   1.20418087
## [401]   1.12755720   0.78619937   0.70963764   0.21181784   0.65039342
## [406]   1.13695208   0.43799628  -1.67259278   0.36550163   0.05904374
## [411]   0.58114647   0.54871526   0.02754893   0.18022987   0.84472130
## [416]  -0.15011103  -0.94319868  -0.17681577  -1.21247875   0.67045226
## [421]  -0.70505273  -0.06490484   0.82591686   0.57180936   0.04046836
## [426]   0.76883248  -0.93848842  -0.43132555   0.51934102   0.83217183
## [431]  -0.12732308   0.28430937   0.83664364   0.89763536   0.27267232
## [436]  -0.78171970   1.00383404  -3.47543102   0.91187529   1.06427400
wholesale_pca$x
##                 PC1           PC2           PC3           PC4          PC5
##   [1,]  -0.19707283 -0.3770084356  0.4339928374 -5.086349e-01 -0.001854585
##   [2,]  -0.45313294 -0.1211597823  0.2609418663 -3.508749e-01  0.040946165
##   [3,]  -0.81180172  1.3273282020  1.5940953009  4.144155e-01 -0.301861199
##   [4,]   0.79342916  0.6658443374 -0.3359082992  2.853570e-01  0.057266232
##   [5,]  -0.11570147  1.0073354473  0.7846578714  3.653701e-01 -0.003812347
##   [6,]   0.14370629 -0.2180994333  0.4452745197 -4.774821e-01 -0.059000770
##   [7,]   0.32567049 -0.6325704892  0.1196417115  1.399425e-01 -0.054904769
##   [8,]  -0.15665440 -0.0331363080  0.4012580200  2.786108e-01  0.032831032
##   [9,]   0.48890741 -0.4938233270  0.2485820432 -1.502553e-02  0.081354092
##  [10,]  -1.62027497 -0.5048683883  0.1499964109  1.363545e-01  0.145687282
##  [11,]  -0.66758413 -0.0238881161 -0.3383420998  4.676957e-01 -0.071596678
##  [12,]   0.92597350 -0.3515756476  0.0822191593  1.100768e-01  0.137720104
##  [13,]  -0.92658585 -0.1074909163  0.7247966859 -4.006276e-01  0.084630659
##  [14,]  -0.82672223 -0.5293360636 -0.4619419906  3.523687e-01  0.011172418
##  [15,]  -0.80858534 -0.3934991730  0.4585439002 -7.316764e-02 -0.020590692
##  [16,]   0.93709140 -0.5308636604  0.2043574976  9.831297e-02  0.032723673
##  [17,]  -0.60479469 -0.6384278916  0.2404058097 -1.647392e-01  0.095547612
##  [18,]   0.33914993  0.5663431002  1.1904730227 -6.896284e-02 -0.095319576
##  [19,]  -0.29126066  0.2233895662  0.4970352941  1.829471e-01  0.135411974
##  [20,]   0.29954840 -0.6312712075  0.0644977021  2.521058e-01  0.228237979
##  [21,]   0.33682556 -0.0861339420  0.4875413015  3.768933e-02 -0.164582644
##  [22,]   1.09654804 -0.0043401285 -0.1497704508  7.141227e-02 -0.040058284
##  [23,]   0.26619036  1.5683970175 -0.2467060883  6.670989e-01 -0.283900004
##  [24,]  -4.58054505  3.8072871727  3.3396697767 -1.130469e+00  0.254755186
##  [25,]  -1.19755447  0.8003953225  0.9263685687  3.438610e-01  0.074691495
##  [26,]   0.15537156 -0.8250948908  0.0157524281  4.829123e-02 -0.122135167
##  [27,]   1.03266607  0.0159926101 -0.0590410608  1.074156e-01  0.037212525
##  [28,]   1.09811094 -0.4373483299  0.2574858397  5.881782e-02  0.095718884
##  [29,]  -3.14687957  0.1506165427  0.8514050232 -2.440491e-01  0.374539040
##  [30,]   0.88052223 -0.2960335906  0.2061557803  1.353125e-02 -0.101725549
##  [31,]  -0.05215116 -0.0007608697  0.5787210362  4.390835e-01  0.330576240
##  [32,]   0.69579690 -0.0888786625  0.1462865658 -2.131695e-01 -0.043052084
##  [33,]   0.98632753 -0.5302711469  0.2387360039  3.962267e-02 -0.032243165
##  [34,]   0.41807632  0.4822328908 -0.4532962679 -1.084847e-01  0.315119579
##  [35,]   1.02591988 -0.4642031406  0.2470086458 -8.541622e-02 -0.021926123
##  [36,]  -0.21643153 -0.7002955975 -0.0286492746  8.763578e-02  0.089179114
##  [37,]   0.24158323  0.6313110592  1.0201656795  2.740459e-01  0.025899292
##  [38,]  -0.97020398 -0.5543555171 -0.1693693299 -2.287695e-01 -0.173107471
##  [39,]  -1.62332525 -0.9046825507  0.0284863528 -6.876237e-01  0.072911071
##  [40,]   0.95272626  1.4991601790 -0.5480032712  3.916575e-01 -0.200711189
##  [41,]   0.08308879  2.0275377344  0.1721111919  4.933808e-01 -0.142283907
##  [42,]   0.25869103  0.1421617102  0.4567992931  3.539627e-01 -0.122343929
##  [43,]  -0.87588116 -1.0635936007 -0.1589398770  1.228399e-01  0.005470463
##  [44,]  -2.00255094 -1.2141592087 -0.4235084566  2.189990e-01  0.292958699
##  [45,]  -0.30164586 -0.8128614625 -0.0610496539 -1.224052e-01 -0.009380470
##  [46,]  -2.83141245  0.3536181366  0.8431308911 -6.720454e-01  0.210311577
##  [47,]  -1.90336183 -0.5432914831 -0.0554886874 -2.103213e-01  0.468640242
##  [48,]  -9.41725404  0.5414621846 -0.4271519661 -1.731283e+00  0.133925231
##  [49,]  -0.44041724 -0.5408300715  0.2274220164  1.858785e-01 -0.085748415
##  [50,]  -3.63590895 -0.9762339518 -0.4172346295 -3.493400e-01 -0.008648759
##  [51,]   0.91517116  0.4104644981  0.1479309633  2.485985e-01 -0.124280227
##  [52,]   0.47041131 -0.6176023581  0.1716656472 -9.969138e-02  0.179345625
##  [53,]   0.34153413 -0.4009520531  0.3295290114  6.842046e-02 -0.084407972
##  [54,]  -0.75096260 -0.7685290601 -0.0652044882 -3.819017e-01 -0.096389717
##  [55,]   1.02036283  0.0487333009  0.1823242891  7.034276e-02 -0.039970438
##  [56,]   0.48573185 -0.3152336743  0.2495333559  1.398177e-02 -0.067490936
##  [57,]  -4.63920836 -0.8901055110 -0.5298270393 -1.038605e+00 -0.819611828
##  [58,]  -0.95925425 -0.7378871248  0.2151100896 -1.012359e-01 -0.479576833
##  [59,]   1.08902399 -0.4058042205  0.2500262845 -1.164280e-01 -0.034073572
##  [60,]   0.02055344 -0.4281666899  0.4332603258  4.625049e-02 -0.005978029
##  [61,]   0.20266611 -0.8307229912  0.0488423661  2.140045e-01 -0.112791726
##  [62,]  -8.37149191 -1.5623789638 -1.1584129243 -1.933842e-01  0.319907948
##  [63,]  -0.04643766 -0.0064623816 -0.3126388497 -6.399385e-02 -0.270890553
##  [64,]  -1.44256223 -0.3881746020 -0.2539083496 -7.828486e-02 -0.117075631
##  [65,]   0.84129649  0.1089106750 -0.1116094122  2.036070e-01 -0.090476223
##  [66,]  -5.88216805 -2.0643796924 -0.7569200156  1.028312e+00 -0.240375986
##  [67,]   0.42975520 -0.8439903706  0.0033292780  3.019871e-01 -0.042364665
##  [68,]  -0.59711484 -0.6209401671 -0.0494590712  1.373610e-01  0.119889933
##  [69,]   0.22115034  0.9618614565  0.1144127302 -2.362520e-01 -0.069370103
##  [70,]   1.02170230 -0.4498752241  0.1528820924 -2.238458e-01 -0.120372633
##  [71,]   0.84070633  1.2369213016 -1.0142299556  1.233516e-01  0.019609630
##  [72,]  -1.73915275  2.8610779436  2.4170622052  2.526060e+00  0.464898413
##  [73,]   0.62067938  0.7050255622 -1.0362899361 -3.073257e-01 -0.169665352
##  [74,]   0.26682334  0.6376948170 -0.8755662868 -1.254282e-01  0.361266482
##  [75,]  -0.04638691 -0.1674522707  0.3416721379 -5.974311e-02  0.280263771
##  [76,]   1.20012549  0.2925598478 -0.1589521213  5.912953e-03 -0.158188044
##  [77,]   0.54017219  0.6274661824 -0.7126274387  3.926234e-03  0.235234832
##  [78,]  -2.77004981 -1.1857563171 -0.3572508458  4.752266e-01  0.244348076
##  [79,]   1.12399443 -0.2721741808 -0.0502825534 -2.452565e-02 -0.008690418
##  [80,]   0.65209963 -0.1635736239  0.4455307307  1.627898e-02 -0.063766052
##  [81,]   1.03868601 -0.4709420234  0.2485400502  9.200612e-02  0.019753232
##  [82,]  -1.10479248 -1.0377605203 -0.1519433582 -3.801156e-02 -0.183875803
##  [83,]  -0.56696336 -0.1897705085  0.5070899455 -1.672162e-01  0.108922971
##  [84,]   1.03054389 -0.1083993421  0.0575018685  1.189421e-02 -0.086393476
##  [85,]   0.39812160 -0.6286896384 -0.0790878932  6.345882e-02 -0.312116534
##  [86,] -12.68123458 -2.9055675082 -1.5301790149  1.109718e+00  0.766109027
##  [87,]  -8.39266413 -0.7648749958 -0.0254756094 -5.643262e+00 -0.986574914
##  [88,]  -0.92068706  3.3879831694  2.5748630597  1.493591e+00 -0.172326436
##  [89,]   1.01342557  0.7716998749 -1.2224864249  1.620546e-01  0.127114509
##  [90,]   0.44301966  0.5731766717  0.4416464506  1.520250e-01  0.111153688
##  [91,]   1.19321062 -0.0368736054 -0.1796662555  4.390303e-02 -0.016938275
##  [92,]   0.80614475  0.8926142932 -0.7902658775  9.552051e-03 -0.091570032
##  [93,]  -5.24057761 -0.1447202035  0.1233521218 -7.733263e-02 -0.687874557
##  [94,]   0.52578694  5.0971997130 -4.2280974876  3.562690e-01 -0.235963847
##  [95,]  -0.79761716 -0.7786843800  0.0650273452 -6.281708e-01 -0.038072173
##  [96,]   0.71560919 -0.4279470962  0.2866668376 -4.319073e-02  0.305115990
##  [97,]   0.24404605 -0.8238016100  0.0398452920  2.543221e-01 -0.058548989
##  [98,]   1.32938626 -0.4629908981  0.1364874089 -1.157487e-02 -0.068943918
##  [99,]   1.32246301 -0.4351711891  0.1309323486  1.898908e-02 -0.058179488
## [100,]   1.02727861  0.2983698332 -0.5129768013 -9.591612e-02 -0.037799311
## [101,]  -1.13082005  0.0296427973  0.0885664798  4.577611e-01 -0.473247863
## [102,]  -1.34423210 -0.4240373165  0.0836781087  1.010917e-02  0.047409545
## [103,]  -0.21246138 -0.1865573632 -0.0137137578  1.731627e-02 -0.260442905
## [104,]   0.06820127  2.4096180816 -1.9396808134  4.447883e-01  0.178855067
## [105,]   0.80468449 -0.3727619490  0.0956486645  3.469641e-02 -0.086245320
## [106,]   0.94469735 -0.1982170834  0.3856879072  1.704796e-01  0.133073495
## [107,]  -0.66901612 -0.6188300049  0.3127463650  3.184159e-01 -0.351635129
## [108,]  -1.47652662 -0.4917273047 -0.2096213973  1.042837e-01 -0.366056895
## [109,]  -0.04077613 -0.3953887590  0.4044253759 -4.101700e-01 -0.011842382
## [110,]  -1.70666698 -0.7445501815 -0.0743597119 -8.805089e-01  1.888181050
## [111,]   0.99983015  0.1048203863  0.2865328374  7.158538e-02 -0.063314112
## [112,]  -1.37687414 -0.6081606384  0.1224336064 -4.770345e-02  0.202325530
## [113,]   0.68923179  1.2798147189 -0.4339000015  1.794542e-01 -0.120975838
## [114,]   0.90109151  0.2079202525  0.1193587893  2.975898e-02 -0.126406650
## [115,]   1.05901888  0.0493188652  0.1474579566  1.006991e-01 -0.020229691
## [116,]   1.05586310 -0.1034380740 -0.0528084643  1.030625e-01  0.051592527
## [117,]   0.94497402 -0.3443957553  0.0458862013 -1.318167e-01  0.081944110
## [118,]   0.63888952 -0.1290378910  0.2358638727 -1.088179e-01  0.200165919
## [119,]   0.94868598  0.3684258484 -0.3442094906  3.215203e-02 -0.045101450
## [120,]   0.98250864  0.1114467083 -0.1886718345 -8.411286e-02 -0.027206760
## [121,]   0.96940760 -0.0240916571  0.1173633154  1.211556e-01  0.083059013
## [122,]   1.00153477 -0.1658860503 -0.0390138016 -2.630435e-01 -0.062843175
## [123,]   1.28120984 -0.1024026325  0.1511531050  8.324730e-02 -0.121160465
## [124,]  -0.18913115 -0.3203897860 -0.1106006465 -7.592123e-01  0.209858651
## [125,]   0.86596557  0.4226150095 -0.1163835099  1.589650e-01 -0.026966052
## [126,]   0.40917867  1.9108688107 -2.0407836107  1.442061e-01  0.194309814
## [127,]   1.01779186  0.6950263922 -0.8546792729 -1.292082e-02 -0.092424266
## [128,]  -0.30277111 -0.0382865069  0.6076499875  1.001440e-02  0.248558255
## [129,]   0.39288434 -0.5444758971  0.2361887980 -8.086403e-01 -0.013436955
## [130,]   1.02620109  0.0404906424  0.3923445875  1.777608e-01 -0.109445886
## [131,]   1.00675513  0.5407968338 -0.4618272530 -7.625720e-02 -0.177348616
## [132,]   1.30343896 -0.4607099296  0.2643065329 -3.356327e-02 -0.100342543
## [133,]   0.95838681 -0.4869393345  0.1881508451 -5.659957e-02 -0.072253726
## [134,]   1.18401500 -0.4471723939  0.2570614765 -3.016307e-02 -0.062315609
## [135,]   1.07458712 -0.3650636260  0.2546463208 -8.959202e-02  0.028826429
## [136,]   1.08937421 -0.3717038493  0.1205741859 -1.843713e-02  0.045760580
## [137,]  -0.11183011  0.3043792045 -0.1516516077 -3.557179e-01 -0.032810349
## [138,]   0.20888553 -0.5275345677  0.1124609346 -5.930183e-01  0.376046862
## [139,]   0.47286002  0.1412503836  0.9606664322  5.895386e-02  0.130678757
## [140,]   0.67212442 -0.2671718542  0.3297977543 -3.097939e-01  0.003832633
## [141,]   0.28796809  0.2251490753  0.4384379673  1.275042e-01  0.208626132
## [142,]  -0.02250288 -0.0922838655  0.6251372899 -1.162354e+00  0.168419794
## [143,]   0.34418432 -0.1711513228 -0.2189102391 -5.212920e-01  0.467973078
## [144,]   1.07654549  0.6940836506 -0.9243576757 -1.694764e-02 -0.137634393
## [145,]   0.93281684 -0.5228990290  0.2694356743 -3.070418e-01 -0.050356643
## [146,]  -3.18443785 -0.7438540221  0.4066323700  1.583661e+00  0.575108123
## [147,]   1.06717252 -0.3397410076  0.2201744068 -9.358929e-02  0.024377222
## [148,]   0.80824332 -0.3302172553  0.1391921066 -1.604844e-01 -0.090258890
## [149,]   1.22430136  0.0871948598 -0.2591661155  4.019766e-02 -0.136947866
## [150,]   1.05447741 -0.1543326372  0.4536170345  5.211853e-02 -0.043550579
## [151,]   1.04333128 -0.2288550227  0.3594012592 -2.596068e-02 -0.035171898
## [152,]   0.84943798 -0.1035340420  0.5836853316 -1.020722e-01 -0.054543391
## [153,]   1.02940017 -0.1547998275 -0.1923899590  2.856667e-03  0.058902303
## [154,]   0.39707127 -0.0168057926  0.5788233217 -7.640874e-01 -0.066660671
## [155,]   1.38885601 -0.5690528884  0.2314207961 -2.124517e-02 -0.091789299
## [156,]  -2.10534411 -0.8790908783  0.1196340531  4.951007e-01 -0.399152538
## [157,]  -0.94690511 -0.3674869252  0.5395080461  7.169925e-01 -0.048400289
## [158,]   0.99393880 -0.0635048487 -0.2020406424  4.515528e-02 -0.065786576
## [159,]  -0.28531006 -0.3541772263  0.2917156994  4.519864e-02 -0.031081093
## [160,]  -1.03017136 -1.0361993602 -0.1707735459  2.128945e-01 -0.193738153
## [161,]  -0.35485260 -0.3853783711  0.3230685951  5.594227e-01  0.157293084
## [162,]   1.14689210  0.0795306282  0.6088149730  1.928414e-01 -0.150608121
## [163,]   0.92036981 -0.1025116285 -0.0397713887 -1.145054e-02  0.113646494
## [164,]  -3.05168162 -1.1166208170 -0.7159845011  1.537208e-01 -0.135355954
## [165,]  -0.14994267 -0.3913717078 -0.2421719977 -2.766832e-01 -0.036986765
## [166,]  -1.80878413  0.0566334496 -0.2422449984  3.512095e-02  0.230965549
## [167,]  -0.54851470  0.0452361851  0.7101191669  3.068431e-01 -0.259912693
## [168,]   0.71052625 -0.4665092314  0.2733552116 -6.900412e-02 -0.132030137
## [169,]   1.24301618 -0.2889456013  0.1342404677 -9.451263e-03 -0.074195145
## [170,]   1.12716773 -0.0936776748  0.0446746742  8.243335e-02  0.015988183
## [171,]  -0.90926104 -0.8317067060 -0.1998028894 -3.331411e-03 -0.147138197
## [172,]  -3.27135965  0.4844985168  1.3117135113 -9.195516e-01 -0.175570118
## [173,]   0.20685284 -0.5580156466  0.2248068955 -1.338342e-01 -0.062418192
## [174,]  -1.58573375 -1.0507762119 -0.2920206050  5.614834e-01 -0.069519512
## [175,]   0.83240063  0.0296716850  0.1511531426  2.142830e-01  0.216354135
## [176,]  -0.53378209 -0.5059735509  0.4009604478 -1.696169e-02  0.110272790
## [177,]   0.23300367  0.4510780875 -0.8435857968 -3.784251e-01  0.091638181
## [178,]   0.34523774  0.2986179690  0.6309155013 -3.748515e-01  0.116635082
## [179,]   0.52247477 -0.3031257221  0.1815526848 -5.867474e-01  0.200947639
## [180,]   0.63766473  0.5699523520  0.1113244841 -1.763475e-01 -0.062042887
## [181,]   0.01290303 -0.0294551255  0.7374726259  1.485187e-02  0.263695260
## [182,]  -3.32956183  3.6298166964 -0.2769640395 -1.248901e+00  0.071987331
## [183,]  -0.68822721 -0.9146602969 -0.0990009318 -1.158184e-01 -0.344501680
## [184,]  -7.47744667 15.7336154455  6.4071500330  1.566581e+00 -0.390933851
## [185,]   1.00703448 -0.6486837093  0.1682726870  5.514838e-02  0.204836624
## [186,]   0.81312626 -0.1310929456  0.0426500561 -6.519887e-01 -0.078055731
## [187,]   1.11229463  0.0242439747 -0.1370615402  1.328789e-01 -0.213249552
## [188,]  -0.24041783  0.0940055884 -0.8447029159 -2.866790e-01  0.072035440
## [189,]  -0.72607631 -0.5535689471 -0.4026667470  6.842392e-02 -0.259887453
## [190,]  -0.78285913 -0.3648986302  0.4627545482 -4.376192e-01  0.080242773
## [191,]   0.74272114  0.5531106755 -0.7682232617 -5.684404e-01 -0.044045398
## [192,]   1.27769586 -0.4528908326  0.1150534175  1.173032e-02 -0.010051253
## [193,]   1.09693599 -0.4344151638  0.2381189714 -4.626280e-02  0.021607927
## [194,]  -0.81285702 -0.8912956579 -0.1963626901  7.383901e-01  0.597568986
## [195,]   1.00169591 -0.2619137189  0.3502776810  1.257535e-01  0.033380504
## [196,]   0.45245343  0.9280037294 -0.5185901798 -1.246246e-01  0.129445254
## [197,]   0.08628883  2.7568111298 -1.8229643830 -1.018957e-01 -0.059879885
## [198,]  -0.39085008 -0.3955405972  0.1964547248  1.120201e-02 -0.014723123
## [199,]   0.66997842 -0.0262749566 -0.1984931057  1.164929e-01  0.283969333
## [200,]   1.02565202 -0.4494088678  0.2308137614 -1.343236e-01 -0.022683101
## [201,]  -2.23900996 -0.5878260801 -0.7085900734  8.764202e-02  0.116989345
## [202,]  -2.99546346 -0.6844705504 -0.6063795435  4.206181e-01 -0.406247403
## [203,]  -0.68180673  1.6877976045  1.1111432584 -1.448361e-01  0.296475108
## [204,]   1.10109815 -0.5880892539  0.1182040110  4.898085e-02 -0.075060624
## [205,]   0.89280368 -0.1557704566  0.2918836756  2.145287e-01  0.247566809
## [206,]  -2.04834810 -1.0164029887 -0.2749671288  1.925170e-01  0.277801549
## [207,]   1.22289397 -0.4091923864  0.1658758384 -1.619192e-02 -0.086383217
## [208,]   0.02999763 -0.4562055716 -0.3960906986  7.069393e-02 -0.444580597
## [209,]   0.29338844 -0.3614455997 -0.0080606821  1.020401e-01 -0.194049088
## [210,]  -2.07821189 -1.0624050684 -0.2629478297  9.111398e-02 -0.702586793
## [211,]   0.95666185  0.1415798527  0.4661520779  8.654914e-02 -0.108537036
## [212,]  -5.65091274 -0.5719339518 -0.7387671291 -1.300213e-01 -0.126122041
## [213,]   1.01303835 -0.0291142686  0.4447647467  1.647516e-01 -0.039979160
## [214,]  -0.07733767 -0.3524530076  0.1631543516 -1.007511e-01 -0.224364938
## [215,]  -0.54162222 -0.6955489007 -0.0163762810  1.424171e-01 -0.152658315
## [216,]  -1.23239191 -0.2683704471  0.2912940521 -1.525642e-02  0.112285888
## [217,]  -3.65784251 -1.5024946145 -0.4451166133  3.442908e-01  0.657875917
## [218,]   1.03509689  0.0266087310  0.1292185239  4.633317e-02 -0.017602064
## [219,]  -1.19058168  0.6205930559  1.2442387713  7.184164e-01  0.142727311
## [220,]   1.25137280 -0.2392367905 -0.0817948446  2.619077e-02 -0.024885647
## [221,]   1.16786662 -0.1694031479  0.1501129365  2.960327e-02 -0.038677735
## [222,]  -0.30619270 -0.8089351138  0.0668910915 -1.868201e-01  0.063360480
## [223,]   1.02353682  0.5442296394 -0.7992298261  8.139072e-02  0.023241419
## [224,]   0.64173440  0.4433723400 -0.3296613548  1.340806e-01  0.105076655
## [225,]   1.19242546 -0.3378506721  0.2671314257  4.137322e-02 -0.022546599
## [226,]   0.74927539 -0.3702922405  0.2832530799 -9.813612e-02  0.063127379
## [227,]  -0.04166179 -0.1845337776  0.1953124055 -4.971583e-03  0.146592921
## [228,]   1.03747427 -0.1018997011  0.0652443951 -9.734645e-02 -0.063282394
## [229,]   0.74782120 -0.6691384055 -0.0398167843  3.062108e-01 -0.753030645
## [230,]   0.82806814  0.5910908116 -0.5551384969 -1.856014e-02 -0.089465542
## [231,]   0.25762310  1.0470755800 -0.5119581753 -1.145021e-01  0.051283570
## [232,]   0.14712185 -0.2486236341  0.1632538632 -9.088454e-01 -0.116555921
## [233,]   0.92806057 -0.3530682004  0.3031763812  2.615664e-02  0.114450635
## [234,]   0.77748264 -0.4430065220  0.1067856518 -4.316804e-01  0.059574527
## [235,]   0.67882658  0.5685557802  0.1896331714  1.585129e-01  0.034903691
## [236,]   0.58424690 -0.3544175668  0.1247594862 -5.103974e-01 -0.111243449
## [237,]   1.07019195 -0.2560573276 -0.0902724213  6.404733e-02  0.048960534
## [238,]   0.93984852  0.4097679695 -0.1117504327 -2.455267e-01 -0.140479637
## [239,]   1.29676093 -0.3771593082  0.1253457821 -1.504406e-02 -0.080820647
## [240,]   0.65211081  0.6117600861 -0.0475416452  1.822848e-01 -0.037125264
## [241,]   0.35751675  1.5650061126 -0.8886851108  2.372639e-01  0.233027565
## [242,]   0.96409594 -0.0619058462  0.1362730091  2.831163e-02 -0.022388607
## [243,]   1.02852505  0.0209240042 -0.2246841232  1.443754e-01 -0.002387319
## [244,]   0.42242573 -0.0883244925  0.6300559875  1.449717e-01 -0.041947263
## [245,]  -0.37409228 -0.2051916783  0.3552773511 -7.683646e-02  0.167212011
## [246,]  -1.17838892 -0.5677000690  0.3926909992  7.040641e-01 -0.434158944
## [247,]   0.99935781 -0.2027092622  0.1142067686 -1.174565e-01 -0.067239648
## [248,]   1.26979462 -0.1376011824  0.0892026613  5.425859e-02 -0.100974997
## [249,]   0.74868436 -0.3609679907  0.3041702147 -4.226251e-01 -0.047178655
## [250,]   0.81396957  0.3749872762 -0.6333171467 -2.174539e-01 -0.138534187
## [251,]   1.04468274 -0.1831538258  0.1467280904 -7.118688e-02 -0.037489850
## [252,]  -5.00768849  0.2866944486 -0.4530671996  4.696430e-01 -0.518324418
## [253,]   0.74545878  0.8487520877 -0.5316791722  2.080796e-01  0.131960206
## [254,]  -0.38605647 -0.3822564073  0.3596740591 -1.697875e-01  1.053331483
## [255,]  -0.70708219  0.9391578638  0.4174818883 -1.347493e+00 -0.181354924
## [256,]   1.18411490  0.0030724566 -0.1056092382  8.228318e-02 -0.039791764
## [257,]   0.63210547 -0.4617583277  0.2382291091 -3.355262e-01  0.201599925
## [258,]   0.60371331  0.1584360306 -0.4021340143  2.429649e-01 -0.537359370
## [259,]   0.51724649  1.0841565656  0.0813394709  3.147487e-02 -0.197104415
## [260,]   0.38236102 -0.0600224883 -0.0825430899 -1.448918e-01  0.252324354
## [261,]   0.77157492 -0.4143575173  0.3222401594 -3.760689e-01 -0.093166151
## [262,]   1.16886889  0.4671003805 -0.6890125078 -7.043557e-03 -0.075260316
## [263,]   1.08603962 -0.3224084602  0.2292812684 -5.347571e-03 -0.065522333
## [264,]   0.50559973 -0.1198310239 -0.4845642221  3.683120e-01 -0.046730481
## [265,]  -1.05801199 -0.7327306364  0.2015378961 -2.695094e-02  0.128243055
## [266,]  -1.65734964  1.7937030127 -0.3176590716 -1.632266e+00  0.531331804
## [267,]  -1.47739059 -0.1772552412  0.1448843315  2.739655e-01  0.750619450
## [268,]   0.72868453  0.7388604273  0.4633191765  4.314102e-01 -0.139527389
## [269,]  -1.21350291 -0.8331254104 -0.1733097803  2.719002e-01  0.427226378
## [270,]   1.23813362 -0.2040031259 -0.1028955543  5.837019e-02 -0.082046653
## [271,]   1.19514203  0.2171972169 -0.5560636672 -3.087829e-02 -0.091495871
## [272,]   0.78067858 -0.0285014779  0.4761824614 -3.323474e-01 -0.080771179
## [273,]   0.26602762 -0.2600598349  0.4141737602 -5.980265e-01  0.329535881
## [274,]   0.86878444  0.5324167641 -0.0225250867 -4.330202e-02 -0.111256960
## [275,]   0.97282972 -0.2621784812  0.3694564929  4.112342e-02 -0.114859043
## [276,]   1.22069804 -0.3548028456  0.2178276618 -1.359238e-01 -0.121674632
## [277,]   0.38108645  0.5359681743  0.1031818081  1.588676e-01  0.228136410
## [278,]   1.07846333  1.8653583443 -2.2187714566  1.341660e-01 -0.237361123
## [279,]   0.87750350  0.5586473422 -0.2976317207  3.982789e-02 -0.030181815
## [280,]  -0.22439955 -0.2780541521  0.2576621230  6.954580e-02  0.028826443
## [281,]   0.92072808 -0.1969571181  0.3540777128 -1.174575e-01  0.008145334
## [282,]   0.04172049 -0.0827385077  0.4799604369 -1.985353e-01 -0.063973268
## [283,]   0.56179348  0.5294798027 -0.3505102112 -3.311987e-02 -0.019932544
## [284,]   0.77559110  1.2246245312 -0.9328150131 -7.866405e-02 -0.107268673
## [285,]  -0.05666773  1.0332866463 -0.6082059064  3.097958e-01  0.613305200
## [286,]   1.07514112 -0.4990147752  0.0360851368  6.764338e-02  0.101806296
## [287,]   0.99534417 -0.3724699669 -0.0025361652 -1.141551e-01 -0.206668238
## [288,]   0.87483219  0.8238467598 -0.7660903317  6.233610e-02 -0.026198954
## [289,]   1.19971862 -0.4370617387  0.1507336728  2.377307e-02 -0.080498744
## [290,]   1.33657531 -0.3792644504  0.0403934684 -1.991985e-02 -0.078747463
## [291,]   0.83674885 -0.2326950986  0.4778908332  7.063094e-02 -0.094983491
## [292,]   0.85316130 -0.0776399639  0.0255349598 -1.724166e-01  0.065639153
## [293,]   0.69360374  0.1417127149 -0.1231390079 -7.944642e-03  0.043145957
## [294,]  -0.93965965 -0.6554126047  0.0144458692 -3.368204e-01 -0.092794885
## [295,]   0.59455930 -0.1573054188  0.4481372130  2.453625e-01  0.214344165
## [296,]   0.66171399 -0.6451195060  0.1053069563  1.281564e-01 -0.038034651
## [297,]   0.90049568 -0.0190226696 -0.0533317316  1.344791e-01  0.026534235
## [298,]   0.25180413 -0.5274174486 -0.0489267035  1.892655e-01 -0.140887343
## [299,]  -0.16562608 -0.5647513335  0.0893655028  2.460353e-01 -0.051401842
## [300,]   1.15462330 -0.5205877239  0.2356021757  9.127424e-05  0.001409648
## [301,]   0.06749116 -0.1726847894  0.4762957660 -8.485776e-02 -0.093726153
## [302,]  -1.87238584 -0.9062380384 -0.4427004461 -1.810361e-01  0.108661941
## [303,]  -0.36075328 -0.8370400050  0.0032583493  2.182948e-01 -0.296139923
## [304,]  -0.89344120 -1.2389830186 -0.3587903929  7.500908e-01 -0.514394929
## [305,]  -2.24170924 -0.9151722866  0.0047365098  1.077483e+00 -0.014103893
## [306,]  -0.57018410 -0.5842186912  0.0578018787 -8.680445e-01 -0.071166812
## [307,]  -1.88935546 -0.5541561209 -0.0993321247 -2.146956e-02  0.333094843
## [308,]   0.92559692 -0.2371239152  0.2679024918 -5.256295e-02  0.020162445
## [309,]   1.05503352 -0.4215247836  0.2968103229  5.963136e-02  0.065581698
## [310,]  -1.82444685 -0.4800857869  0.0137381216 -1.292307e+00 -0.197719739
## [311,]   0.91380091  1.4544571140 -1.3567395155  1.620224e-01 -0.067659925
## [312,]   0.64646544 -0.2336199078 -0.2728305098  5.699709e-02  0.444370877
## [313,]  -2.05651935 -1.5961639143 -0.8061189963  1.441392e+00 -1.124041662
## [314,]   1.10515579  0.0942827022 -0.3658363964  4.389359e-02  0.019092121
## [315,]   0.58629339 -0.2366852388  0.1994980699  2.435903e-01  0.306900770
## [316,]  -1.18632311  0.1134601388  0.8352376886 -6.227835e-01  0.062245747
## [317,]   1.04565960  0.0243938808  0.0831196910  4.934935e-02  0.003501565
## [318,]   0.55882703 -0.1724359049  0.4057778341  8.754597e-02  0.179102456
## [319,]   0.88204365 -0.3180530565 -0.0985570540 -1.318735e-01  0.041084475
## [320,]  -3.11235419 -0.6616337617  0.0320866751 -1.164397e+00 -0.730470849
## [321,]   0.88439078 -0.3152197306  0.3659850754 -2.408060e-01 -0.013520147
## [322,]   0.80386112 -0.0072506990  0.0513815263  1.045981e-01  0.204073016
## [323,]   0.92745036 -0.1201143087 -0.3393779899  1.744727e-01 -0.088752154
## [324,]   0.37271862 -0.5907448216  0.0313892316  4.454996e-01  0.516413252
## [325,]   0.85971976  0.0136909553  0.1573108564 -1.846572e-01  0.003240288
## [326,]  -1.78946833  9.4426161661 -7.3561656089 -1.262653e-01  0.172452266
## [327,]   1.05267151  0.0916580173 -0.0880866187  2.103203e-03 -0.098249788
## [328,]   1.17723864 -0.4219320559  0.2890068608  1.941328e-03 -0.008117440
## [329,]   0.81408444  0.8645867977 -0.5709617552  1.088298e-01  0.029775378
## [330,]   0.85138951  0.2466297340 -0.3962137780  1.314342e-01  0.121544020
## [331,]   0.81990469  0.1028458245 -0.0887119701  1.122326e-01  0.204217975
## [332,]  -2.55569469 -0.9119772593 -0.2422695809  1.565106e-02  0.445203963
## [333,]   0.81764691  0.3357835077  0.5424978555 -2.891576e-03 -0.118900424
## [334,]  -7.61379702 -3.4878261273 -1.8570054614  4.487063e+00 -0.492430881
## [335,]   0.73733540  1.8203153674 -0.6665945815  4.988941e-01 -0.104095182
## [336,]  -0.43016311 -0.2108130517  0.3183683323  1.198782e-01  0.026361034
## [337,]   1.12215088 -0.3190418064  0.3242381916 -4.171648e-02 -0.053885459
## [338,]   0.95236916  0.7486749232 -0.7833034255  1.236485e-01 -0.040856249
## [339,]   0.77302224  1.6893212630 -1.9971202384  3.868789e-01  0.331097800
## [340,]   0.67925139  1.1382025886 -0.7816151404  3.759789e-01  0.111049057
## [341,]  -0.44952190 -0.7286057941  0.1357307410  5.248944e-01 -0.468668348
## [342,]  -0.49874907 -0.3767392711  0.3492630012  3.240041e-01 -0.081203551
## [343,]  -0.03297929 -0.5029489774  0.3096893528  1.177555e-02 -0.379628062
## [344,]  -2.53250139 -1.5660071985 -0.8480530559  1.184938e+00 -0.359835221
## [345,]   1.13340753 -0.1952182547 -0.0133121117 -1.458200e-02 -0.026484205
## [346,]   0.22596844 -0.7694471361  0.0206476758  2.730768e-01 -0.041278788
## [347,]  -0.94277386 -0.4648303557 -0.2772970552  3.357660e-01  0.052682251
## [348,]  -0.52623469 -0.2992166497 -0.1906294560  5.170232e-02  0.090517992
## [349,]   0.89883641 -0.3013837867  0.1566870505 -4.785936e-02 -0.155021430
## [350,]  -2.40481023 -0.9960767917 -0.5310822389 -4.374715e-02 -0.394974382
## [351,]   1.08068712 -0.1237118941  0.1927739106  6.405186e-02 -0.016769761
## [352,]  -2.45061408 -0.5584735441  0.0419149034  8.628946e-01 -0.367013462
## [353,]   1.19422964 -0.4293999671  0.1558240037 -5.857045e-02 -0.012704664
## [354,]  -1.46109306 -1.0443346120 -0.0859166808  7.205129e-01  0.203389284
## [355,]   0.29654054  0.8630742744 -0.1383954212 -3.401633e-01 -0.240078342
## [356,]   1.19246382 -0.5482961618  0.2104436785 -7.319833e-03  0.017614488
## [357,]   1.30670647 -0.0029419227 -0.0920076981  6.454974e-02 -0.118117924
## [358,]  -0.84837304 -1.2653251323 -0.3054295861  1.059554e+00  0.619631964
## [359,]  -0.53430822  1.4509195863  0.4951650461 -1.488780e+00 -0.307004553
## [360,]   0.74548879 -0.3141877231  0.4084485713 -5.018286e-01 -0.030554517
## [361,]   0.95060230 -0.1063642743 -0.0303243494 -1.610490e-01 -0.059279836
## [362,]   1.24298882 -0.3289021623  0.1503307078  8.015338e-03 -0.078577675
## [363,]   1.04927604 -0.3656586146  0.3065814927 -2.120530e-02  0.028795306
## [364,]   0.87486904 -0.6155984555  0.1869141366  1.449102e-01  0.031142672
## [365,]   1.13722957 -0.3566829731  0.1603429922  3.141357e-02 -0.081879125
## [366,]  -0.34134077  0.0528651642  0.5204387607  2.484323e-01 -0.266636410
## [367,]   1.06478454 -0.3160073629  0.1713890889 -1.369749e-01 -0.037004496
## [368,]   1.23457189 -0.3020715155  0.1031540306 -3.290657e-02 -0.118323974
## [369,]   1.09202865 -0.1860571487  0.0523766298  1.397055e-02  0.035019264
## [370,]   1.29790056 -0.3646317914  0.1456950323  1.026699e-02 -0.070216959
## [371,]   0.54728205  0.0660108492  0.5275880023  4.670435e-03  0.109653457
## [372,]   0.92861428  0.7341864175 -0.7960212484  5.201769e-02 -0.132267223
## [373,]   0.55848361  0.6329891063  1.2548922421  1.947481e-01 -0.193946445
## [374,]  -0.01036762  0.1984867185  0.6528332213  2.705561e-02  0.057534446
## [375,]   1.02837629 -0.2211011595  0.1777392160 -1.044276e-01 -0.058081877
## [376,]   1.15932849 -0.5015726865  0.1543070714 -9.802522e-02 -0.093532531
## [377,]  -0.77356526  0.1996188872 -0.5105311814  8.662076e-03  0.146226030
## [378,]   0.88358086 -0.1532556029  0.3813297561 -1.293612e-01  0.029117565
## [379,]   0.93923945 -0.2746083703  0.4739350118 -1.933370e-01 -0.016908645
## [380,]   0.27600519 -0.6575609068  0.1558497541 -1.804023e-01  0.539501791
## [381,]   1.07810889 -0.0128717819 -0.3024832323  5.457804e-02 -0.056683715
## [382,]   0.81131596  1.0058196043 -1.0577260590 -3.067384e-01 -0.107566207
## [383,]  -0.12863861  0.3117748537  0.4582050708 -9.939952e-02  0.162220332
## [384,]   0.98212572  0.0222401601 -0.3036920467  4.719205e-02  0.066127080
## [385,]  -1.64808006  1.1586559064  0.9605663032 -1.324026e+00  0.742990749
## [386,]   1.10233193  0.0088755009  0.0972514015  8.876743e-02 -0.053949151
## [387,]   0.82259230 -0.0935972530  0.1765052575 -1.786855e-01  0.008277633
## [388,]   1.04129188 -0.0912372095  0.1742296693 -3.926493e-02 -0.062097721
## [389,]   1.19768522 -0.2641713568  0.0789849464 -1.220946e-03 -0.064952858
## [390,]   1.09437876 -0.0030619385 -0.0478148524 -2.252481e-02 -0.068766279
## [391,]   1.06891237  0.4179833336 -0.3424848203  7.987405e-02 -0.108186282
## [392,]   0.88438236 -0.0417631467  0.5367800244 -3.089990e-02 -0.009649391
## [393,]   0.79981986 -0.3397531358  0.2968846699 -2.819700e-01  0.110441519
## [394,]   0.48759544  0.8695421826 -0.8090023384 -4.435117e-01  0.028695796
## [395,]   1.07628493 -0.3243979663  0.1054144579  6.200560e-02  0.097367055
## [396,]   1.08292394 -0.1408151659 -0.1508761886 -5.685268e-03 -0.156053509
## [397,]  -0.65441107  0.1365619541  0.2609186633 -5.374683e-01 -0.017928094
## [398,]   1.06672699  0.5739678319 -0.5833083159 -5.032264e-03 -0.068046024
## [399,]   1.21812567  0.2573167088 -0.4850298560 -3.179681e-02 -0.108576616
## [400,]   1.20418087 -0.2977446541  0.0719496515  3.635687e-02 -0.118696408
## [401,]   1.12755720  0.1486469749 -0.0539299714  7.907698e-02 -0.080788486
## [402,]   0.78619937  1.7607701632 -1.2401567867  8.773626e-02 -0.092231125
## [403,]   0.70963764 -0.4824173163  0.2787551961 -3.455904e-01  0.247948235
## [404,]   0.21181784 -0.4378501159  0.3382349083 -1.023084e+00  0.087221718
## [405,]   0.65039342  0.1682494910 -0.2479710243 -2.358100e-01 -0.038949793
## [406,]   1.13695208 -0.2329491833  0.0020048404  5.289853e-03 -0.124123853
## [407,]   0.43799628  0.9861577681 -1.0141918729 -1.341328e-01  0.017341293
## [408,]  -1.67259278 -0.5997607604 -0.4539003847 -1.927750e-01  0.088799367
## [409,]   0.36550163 -0.4654167058 -0.0653570248  4.368427e-03 -0.044121872
## [410,]   0.05904374  0.7407264885  0.9812353376  5.321543e-01 -0.116912163
## [411,]   0.58114647 -0.1053616044  0.3728519656  2.555079e-01 -0.091531240
## [412,]   0.54871526  0.5993113197  1.0280690648  2.474061e-01 -0.033336374
## [413,]   0.02754893 -0.8683954018  0.0009452655  2.004207e-01  0.396172149
## [414,]   0.18022987  2.4627986053 -1.8610262286  1.696222e-01  0.081699407
## [415,]   0.84472130  0.2166544351 -0.5858918678  3.730761e-02 -0.052819470
## [416,]  -0.15011103 -0.1654789686  0.2521128931  6.515206e-02 -0.052293459
## [417,]  -0.94319868 -0.6282524920  0.0694434201 -2.856556e-01 -0.328750555
## [418,]  -0.17681577 -0.5846549679  0.2174968459  9.846607e-02  0.179411157
## [419,]  -1.21247875 -0.9451190928 -0.0111536007  2.085788e-01  0.281727286
## [420,]   0.67045226 -0.2169645295  0.4594481571 -7.930226e-02 -0.225166310
## [421,]  -0.70505273 -0.7893865579  0.1792825081  4.685864e-01 -0.138527213
## [422,]  -0.06490484 -0.3007384881  0.3109499418  1.898877e-01  0.016876618
## [423,]   0.82591686 -0.2892677213  0.3292781858  1.754135e-01  0.035366768
## [424,]   0.57180936 -0.3995984651  0.1544486982 -6.623976e-02 -0.049472294
## [425,]   0.04046836 -0.7367264203 -0.0847164943  3.219454e-01  0.343336774
## [426,]   0.76883248  2.0500342258 -1.5657601158  1.670196e-01 -0.067827419
## [427,]  -0.93848842 -0.0821362098 -0.0534415939  1.076078e-02  0.138959378
## [428,]  -0.43132555  2.0067711242 -1.5734003459 -1.398859e+00  0.039329073
## [429,]   0.51934102 -0.2273851246 -0.0315692426 -4.106207e-01  0.096672075
## [430,]   0.83217183 -0.0517546591  0.7913966759  1.911758e-01  0.080207639
## [431,]  -0.12732308 -0.2510251070  0.4661498794  3.030175e-01  1.035711609
## [432,]   0.28430937  1.6278170123 -1.4322862099 -6.732602e-02 -0.051096480
## [433,]   0.83664364 -0.5884685158  0.1925679473  1.462679e-01  0.052584928
## [434,]   0.89763536 -0.0286593561  0.3618008079 -1.269600e-01 -0.105069502
## [435,]   0.27267232 -0.4987640539  0.1838051451  7.266804e-02  0.119401988
## [436,]  -0.78171970  1.7262064236 -1.2339946527 -4.534560e-01  0.892440952
## [437,]   1.00383404  0.6000966110  0.1372499975  1.617472e-01 -0.153667550
## [438,]  -3.47543102 -1.2015869428 -0.1938524404  5.134742e-01 -0.065875377
## [439,]   0.91187529  0.0286815529  0.5761825595  9.421507e-02 -0.030771798
## [440,]   1.06427400 -0.6008476585  0.2126003922 -8.899895e-02  0.011009682
plot(wholesale_pca$x,xlim=xlim,ylim=xlim)

wholesale_pca$rotation[,1]
##             Milk          Grocery           Frozen Detergents_Paper 
##      -0.54363795      -0.58193330      -0.03962544      -0.55369302 
##       Delicassen 
##      -0.24013597
wholesale_pca$rotation
##                          PC1        PC2         PC3         PC4         PC5
## Milk             -0.54363795  0.1146154  0.09014458 -0.82543534 -0.04302952
## Grocery          -0.58193330 -0.1556719 -0.12777739  0.30993371  0.72438520
## Frozen           -0.03962544  0.7024176 -0.70857828  0.04761674 -0.02624427
## Detergents_Paper -0.55369302 -0.2718776 -0.19028739  0.34173928 -0.68301653
## Delicassen       -0.24013597  0.6287461  0.66125216  0.32178331 -0.07883018
plot(wholesale[,-1])

wholesale_pca$x
##                 PC1           PC2           PC3           PC4          PC5
##   [1,]  -0.19707283 -0.3770084356  0.4339928374 -5.086349e-01 -0.001854585
##   [2,]  -0.45313294 -0.1211597823  0.2609418663 -3.508749e-01  0.040946165
##   [3,]  -0.81180172  1.3273282020  1.5940953009  4.144155e-01 -0.301861199
##   [4,]   0.79342916  0.6658443374 -0.3359082992  2.853570e-01  0.057266232
##   [5,]  -0.11570147  1.0073354473  0.7846578714  3.653701e-01 -0.003812347
##   [6,]   0.14370629 -0.2180994333  0.4452745197 -4.774821e-01 -0.059000770
##   [7,]   0.32567049 -0.6325704892  0.1196417115  1.399425e-01 -0.054904769
##   [8,]  -0.15665440 -0.0331363080  0.4012580200  2.786108e-01  0.032831032
##   [9,]   0.48890741 -0.4938233270  0.2485820432 -1.502553e-02  0.081354092
##  [10,]  -1.62027497 -0.5048683883  0.1499964109  1.363545e-01  0.145687282
##  [11,]  -0.66758413 -0.0238881161 -0.3383420998  4.676957e-01 -0.071596678
##  [12,]   0.92597350 -0.3515756476  0.0822191593  1.100768e-01  0.137720104
##  [13,]  -0.92658585 -0.1074909163  0.7247966859 -4.006276e-01  0.084630659
##  [14,]  -0.82672223 -0.5293360636 -0.4619419906  3.523687e-01  0.011172418
##  [15,]  -0.80858534 -0.3934991730  0.4585439002 -7.316764e-02 -0.020590692
##  [16,]   0.93709140 -0.5308636604  0.2043574976  9.831297e-02  0.032723673
##  [17,]  -0.60479469 -0.6384278916  0.2404058097 -1.647392e-01  0.095547612
##  [18,]   0.33914993  0.5663431002  1.1904730227 -6.896284e-02 -0.095319576
##  [19,]  -0.29126066  0.2233895662  0.4970352941  1.829471e-01  0.135411974
##  [20,]   0.29954840 -0.6312712075  0.0644977021  2.521058e-01  0.228237979
##  [21,]   0.33682556 -0.0861339420  0.4875413015  3.768933e-02 -0.164582644
##  [22,]   1.09654804 -0.0043401285 -0.1497704508  7.141227e-02 -0.040058284
##  [23,]   0.26619036  1.5683970175 -0.2467060883  6.670989e-01 -0.283900004
##  [24,]  -4.58054505  3.8072871727  3.3396697767 -1.130469e+00  0.254755186
##  [25,]  -1.19755447  0.8003953225  0.9263685687  3.438610e-01  0.074691495
##  [26,]   0.15537156 -0.8250948908  0.0157524281  4.829123e-02 -0.122135167
##  [27,]   1.03266607  0.0159926101 -0.0590410608  1.074156e-01  0.037212525
##  [28,]   1.09811094 -0.4373483299  0.2574858397  5.881782e-02  0.095718884
##  [29,]  -3.14687957  0.1506165427  0.8514050232 -2.440491e-01  0.374539040
##  [30,]   0.88052223 -0.2960335906  0.2061557803  1.353125e-02 -0.101725549
##  [31,]  -0.05215116 -0.0007608697  0.5787210362  4.390835e-01  0.330576240
##  [32,]   0.69579690 -0.0888786625  0.1462865658 -2.131695e-01 -0.043052084
##  [33,]   0.98632753 -0.5302711469  0.2387360039  3.962267e-02 -0.032243165
##  [34,]   0.41807632  0.4822328908 -0.4532962679 -1.084847e-01  0.315119579
##  [35,]   1.02591988 -0.4642031406  0.2470086458 -8.541622e-02 -0.021926123
##  [36,]  -0.21643153 -0.7002955975 -0.0286492746  8.763578e-02  0.089179114
##  [37,]   0.24158323  0.6313110592  1.0201656795  2.740459e-01  0.025899292
##  [38,]  -0.97020398 -0.5543555171 -0.1693693299 -2.287695e-01 -0.173107471
##  [39,]  -1.62332525 -0.9046825507  0.0284863528 -6.876237e-01  0.072911071
##  [40,]   0.95272626  1.4991601790 -0.5480032712  3.916575e-01 -0.200711189
##  [41,]   0.08308879  2.0275377344  0.1721111919  4.933808e-01 -0.142283907
##  [42,]   0.25869103  0.1421617102  0.4567992931  3.539627e-01 -0.122343929
##  [43,]  -0.87588116 -1.0635936007 -0.1589398770  1.228399e-01  0.005470463
##  [44,]  -2.00255094 -1.2141592087 -0.4235084566  2.189990e-01  0.292958699
##  [45,]  -0.30164586 -0.8128614625 -0.0610496539 -1.224052e-01 -0.009380470
##  [46,]  -2.83141245  0.3536181366  0.8431308911 -6.720454e-01  0.210311577
##  [47,]  -1.90336183 -0.5432914831 -0.0554886874 -2.103213e-01  0.468640242
##  [48,]  -9.41725404  0.5414621846 -0.4271519661 -1.731283e+00  0.133925231
##  [49,]  -0.44041724 -0.5408300715  0.2274220164  1.858785e-01 -0.085748415
##  [50,]  -3.63590895 -0.9762339518 -0.4172346295 -3.493400e-01 -0.008648759
##  [51,]   0.91517116  0.4104644981  0.1479309633  2.485985e-01 -0.124280227
##  [52,]   0.47041131 -0.6176023581  0.1716656472 -9.969138e-02  0.179345625
##  [53,]   0.34153413 -0.4009520531  0.3295290114  6.842046e-02 -0.084407972
##  [54,]  -0.75096260 -0.7685290601 -0.0652044882 -3.819017e-01 -0.096389717
##  [55,]   1.02036283  0.0487333009  0.1823242891  7.034276e-02 -0.039970438
##  [56,]   0.48573185 -0.3152336743  0.2495333559  1.398177e-02 -0.067490936
##  [57,]  -4.63920836 -0.8901055110 -0.5298270393 -1.038605e+00 -0.819611828
##  [58,]  -0.95925425 -0.7378871248  0.2151100896 -1.012359e-01 -0.479576833
##  [59,]   1.08902399 -0.4058042205  0.2500262845 -1.164280e-01 -0.034073572
##  [60,]   0.02055344 -0.4281666899  0.4332603258  4.625049e-02 -0.005978029
##  [61,]   0.20266611 -0.8307229912  0.0488423661  2.140045e-01 -0.112791726
##  [62,]  -8.37149191 -1.5623789638 -1.1584129243 -1.933842e-01  0.319907948
##  [63,]  -0.04643766 -0.0064623816 -0.3126388497 -6.399385e-02 -0.270890553
##  [64,]  -1.44256223 -0.3881746020 -0.2539083496 -7.828486e-02 -0.117075631
##  [65,]   0.84129649  0.1089106750 -0.1116094122  2.036070e-01 -0.090476223
##  [66,]  -5.88216805 -2.0643796924 -0.7569200156  1.028312e+00 -0.240375986
##  [67,]   0.42975520 -0.8439903706  0.0033292780  3.019871e-01 -0.042364665
##  [68,]  -0.59711484 -0.6209401671 -0.0494590712  1.373610e-01  0.119889933
##  [69,]   0.22115034  0.9618614565  0.1144127302 -2.362520e-01 -0.069370103
##  [70,]   1.02170230 -0.4498752241  0.1528820924 -2.238458e-01 -0.120372633
##  [71,]   0.84070633  1.2369213016 -1.0142299556  1.233516e-01  0.019609630
##  [72,]  -1.73915275  2.8610779436  2.4170622052  2.526060e+00  0.464898413
##  [73,]   0.62067938  0.7050255622 -1.0362899361 -3.073257e-01 -0.169665352
##  [74,]   0.26682334  0.6376948170 -0.8755662868 -1.254282e-01  0.361266482
##  [75,]  -0.04638691 -0.1674522707  0.3416721379 -5.974311e-02  0.280263771
##  [76,]   1.20012549  0.2925598478 -0.1589521213  5.912953e-03 -0.158188044
##  [77,]   0.54017219  0.6274661824 -0.7126274387  3.926234e-03  0.235234832
##  [78,]  -2.77004981 -1.1857563171 -0.3572508458  4.752266e-01  0.244348076
##  [79,]   1.12399443 -0.2721741808 -0.0502825534 -2.452565e-02 -0.008690418
##  [80,]   0.65209963 -0.1635736239  0.4455307307  1.627898e-02 -0.063766052
##  [81,]   1.03868601 -0.4709420234  0.2485400502  9.200612e-02  0.019753232
##  [82,]  -1.10479248 -1.0377605203 -0.1519433582 -3.801156e-02 -0.183875803
##  [83,]  -0.56696336 -0.1897705085  0.5070899455 -1.672162e-01  0.108922971
##  [84,]   1.03054389 -0.1083993421  0.0575018685  1.189421e-02 -0.086393476
##  [85,]   0.39812160 -0.6286896384 -0.0790878932  6.345882e-02 -0.312116534
##  [86,] -12.68123458 -2.9055675082 -1.5301790149  1.109718e+00  0.766109027
##  [87,]  -8.39266413 -0.7648749958 -0.0254756094 -5.643262e+00 -0.986574914
##  [88,]  -0.92068706  3.3879831694  2.5748630597  1.493591e+00 -0.172326436
##  [89,]   1.01342557  0.7716998749 -1.2224864249  1.620546e-01  0.127114509
##  [90,]   0.44301966  0.5731766717  0.4416464506  1.520250e-01  0.111153688
##  [91,]   1.19321062 -0.0368736054 -0.1796662555  4.390303e-02 -0.016938275
##  [92,]   0.80614475  0.8926142932 -0.7902658775  9.552051e-03 -0.091570032
##  [93,]  -5.24057761 -0.1447202035  0.1233521218 -7.733263e-02 -0.687874557
##  [94,]   0.52578694  5.0971997130 -4.2280974876  3.562690e-01 -0.235963847
##  [95,]  -0.79761716 -0.7786843800  0.0650273452 -6.281708e-01 -0.038072173
##  [96,]   0.71560919 -0.4279470962  0.2866668376 -4.319073e-02  0.305115990
##  [97,]   0.24404605 -0.8238016100  0.0398452920  2.543221e-01 -0.058548989
##  [98,]   1.32938626 -0.4629908981  0.1364874089 -1.157487e-02 -0.068943918
##  [99,]   1.32246301 -0.4351711891  0.1309323486  1.898908e-02 -0.058179488
## [100,]   1.02727861  0.2983698332 -0.5129768013 -9.591612e-02 -0.037799311
## [101,]  -1.13082005  0.0296427973  0.0885664798  4.577611e-01 -0.473247863
## [102,]  -1.34423210 -0.4240373165  0.0836781087  1.010917e-02  0.047409545
## [103,]  -0.21246138 -0.1865573632 -0.0137137578  1.731627e-02 -0.260442905
## [104,]   0.06820127  2.4096180816 -1.9396808134  4.447883e-01  0.178855067
## [105,]   0.80468449 -0.3727619490  0.0956486645  3.469641e-02 -0.086245320
## [106,]   0.94469735 -0.1982170834  0.3856879072  1.704796e-01  0.133073495
## [107,]  -0.66901612 -0.6188300049  0.3127463650  3.184159e-01 -0.351635129
## [108,]  -1.47652662 -0.4917273047 -0.2096213973  1.042837e-01 -0.366056895
## [109,]  -0.04077613 -0.3953887590  0.4044253759 -4.101700e-01 -0.011842382
## [110,]  -1.70666698 -0.7445501815 -0.0743597119 -8.805089e-01  1.888181050
## [111,]   0.99983015  0.1048203863  0.2865328374  7.158538e-02 -0.063314112
## [112,]  -1.37687414 -0.6081606384  0.1224336064 -4.770345e-02  0.202325530
## [113,]   0.68923179  1.2798147189 -0.4339000015  1.794542e-01 -0.120975838
## [114,]   0.90109151  0.2079202525  0.1193587893  2.975898e-02 -0.126406650
## [115,]   1.05901888  0.0493188652  0.1474579566  1.006991e-01 -0.020229691
## [116,]   1.05586310 -0.1034380740 -0.0528084643  1.030625e-01  0.051592527
## [117,]   0.94497402 -0.3443957553  0.0458862013 -1.318167e-01  0.081944110
## [118,]   0.63888952 -0.1290378910  0.2358638727 -1.088179e-01  0.200165919
## [119,]   0.94868598  0.3684258484 -0.3442094906  3.215203e-02 -0.045101450
## [120,]   0.98250864  0.1114467083 -0.1886718345 -8.411286e-02 -0.027206760
## [121,]   0.96940760 -0.0240916571  0.1173633154  1.211556e-01  0.083059013
## [122,]   1.00153477 -0.1658860503 -0.0390138016 -2.630435e-01 -0.062843175
## [123,]   1.28120984 -0.1024026325  0.1511531050  8.324730e-02 -0.121160465
## [124,]  -0.18913115 -0.3203897860 -0.1106006465 -7.592123e-01  0.209858651
## [125,]   0.86596557  0.4226150095 -0.1163835099  1.589650e-01 -0.026966052
## [126,]   0.40917867  1.9108688107 -2.0407836107  1.442061e-01  0.194309814
## [127,]   1.01779186  0.6950263922 -0.8546792729 -1.292082e-02 -0.092424266
## [128,]  -0.30277111 -0.0382865069  0.6076499875  1.001440e-02  0.248558255
## [129,]   0.39288434 -0.5444758971  0.2361887980 -8.086403e-01 -0.013436955
## [130,]   1.02620109  0.0404906424  0.3923445875  1.777608e-01 -0.109445886
## [131,]   1.00675513  0.5407968338 -0.4618272530 -7.625720e-02 -0.177348616
## [132,]   1.30343896 -0.4607099296  0.2643065329 -3.356327e-02 -0.100342543
## [133,]   0.95838681 -0.4869393345  0.1881508451 -5.659957e-02 -0.072253726
## [134,]   1.18401500 -0.4471723939  0.2570614765 -3.016307e-02 -0.062315609
## [135,]   1.07458712 -0.3650636260  0.2546463208 -8.959202e-02  0.028826429
## [136,]   1.08937421 -0.3717038493  0.1205741859 -1.843713e-02  0.045760580
## [137,]  -0.11183011  0.3043792045 -0.1516516077 -3.557179e-01 -0.032810349
## [138,]   0.20888553 -0.5275345677  0.1124609346 -5.930183e-01  0.376046862
## [139,]   0.47286002  0.1412503836  0.9606664322  5.895386e-02  0.130678757
## [140,]   0.67212442 -0.2671718542  0.3297977543 -3.097939e-01  0.003832633
## [141,]   0.28796809  0.2251490753  0.4384379673  1.275042e-01  0.208626132
## [142,]  -0.02250288 -0.0922838655  0.6251372899 -1.162354e+00  0.168419794
## [143,]   0.34418432 -0.1711513228 -0.2189102391 -5.212920e-01  0.467973078
## [144,]   1.07654549  0.6940836506 -0.9243576757 -1.694764e-02 -0.137634393
## [145,]   0.93281684 -0.5228990290  0.2694356743 -3.070418e-01 -0.050356643
## [146,]  -3.18443785 -0.7438540221  0.4066323700  1.583661e+00  0.575108123
## [147,]   1.06717252 -0.3397410076  0.2201744068 -9.358929e-02  0.024377222
## [148,]   0.80824332 -0.3302172553  0.1391921066 -1.604844e-01 -0.090258890
## [149,]   1.22430136  0.0871948598 -0.2591661155  4.019766e-02 -0.136947866
## [150,]   1.05447741 -0.1543326372  0.4536170345  5.211853e-02 -0.043550579
## [151,]   1.04333128 -0.2288550227  0.3594012592 -2.596068e-02 -0.035171898
## [152,]   0.84943798 -0.1035340420  0.5836853316 -1.020722e-01 -0.054543391
## [153,]   1.02940017 -0.1547998275 -0.1923899590  2.856667e-03  0.058902303
## [154,]   0.39707127 -0.0168057926  0.5788233217 -7.640874e-01 -0.066660671
## [155,]   1.38885601 -0.5690528884  0.2314207961 -2.124517e-02 -0.091789299
## [156,]  -2.10534411 -0.8790908783  0.1196340531  4.951007e-01 -0.399152538
## [157,]  -0.94690511 -0.3674869252  0.5395080461  7.169925e-01 -0.048400289
## [158,]   0.99393880 -0.0635048487 -0.2020406424  4.515528e-02 -0.065786576
## [159,]  -0.28531006 -0.3541772263  0.2917156994  4.519864e-02 -0.031081093
## [160,]  -1.03017136 -1.0361993602 -0.1707735459  2.128945e-01 -0.193738153
## [161,]  -0.35485260 -0.3853783711  0.3230685951  5.594227e-01  0.157293084
## [162,]   1.14689210  0.0795306282  0.6088149730  1.928414e-01 -0.150608121
## [163,]   0.92036981 -0.1025116285 -0.0397713887 -1.145054e-02  0.113646494
## [164,]  -3.05168162 -1.1166208170 -0.7159845011  1.537208e-01 -0.135355954
## [165,]  -0.14994267 -0.3913717078 -0.2421719977 -2.766832e-01 -0.036986765
## [166,]  -1.80878413  0.0566334496 -0.2422449984  3.512095e-02  0.230965549
## [167,]  -0.54851470  0.0452361851  0.7101191669  3.068431e-01 -0.259912693
## [168,]   0.71052625 -0.4665092314  0.2733552116 -6.900412e-02 -0.132030137
## [169,]   1.24301618 -0.2889456013  0.1342404677 -9.451263e-03 -0.074195145
## [170,]   1.12716773 -0.0936776748  0.0446746742  8.243335e-02  0.015988183
## [171,]  -0.90926104 -0.8317067060 -0.1998028894 -3.331411e-03 -0.147138197
## [172,]  -3.27135965  0.4844985168  1.3117135113 -9.195516e-01 -0.175570118
## [173,]   0.20685284 -0.5580156466  0.2248068955 -1.338342e-01 -0.062418192
## [174,]  -1.58573375 -1.0507762119 -0.2920206050  5.614834e-01 -0.069519512
## [175,]   0.83240063  0.0296716850  0.1511531426  2.142830e-01  0.216354135
## [176,]  -0.53378209 -0.5059735509  0.4009604478 -1.696169e-02  0.110272790
## [177,]   0.23300367  0.4510780875 -0.8435857968 -3.784251e-01  0.091638181
## [178,]   0.34523774  0.2986179690  0.6309155013 -3.748515e-01  0.116635082
## [179,]   0.52247477 -0.3031257221  0.1815526848 -5.867474e-01  0.200947639
## [180,]   0.63766473  0.5699523520  0.1113244841 -1.763475e-01 -0.062042887
## [181,]   0.01290303 -0.0294551255  0.7374726259  1.485187e-02  0.263695260
## [182,]  -3.32956183  3.6298166964 -0.2769640395 -1.248901e+00  0.071987331
## [183,]  -0.68822721 -0.9146602969 -0.0990009318 -1.158184e-01 -0.344501680
## [184,]  -7.47744667 15.7336154455  6.4071500330  1.566581e+00 -0.390933851
## [185,]   1.00703448 -0.6486837093  0.1682726870  5.514838e-02  0.204836624
## [186,]   0.81312626 -0.1310929456  0.0426500561 -6.519887e-01 -0.078055731
## [187,]   1.11229463  0.0242439747 -0.1370615402  1.328789e-01 -0.213249552
## [188,]  -0.24041783  0.0940055884 -0.8447029159 -2.866790e-01  0.072035440
## [189,]  -0.72607631 -0.5535689471 -0.4026667470  6.842392e-02 -0.259887453
## [190,]  -0.78285913 -0.3648986302  0.4627545482 -4.376192e-01  0.080242773
## [191,]   0.74272114  0.5531106755 -0.7682232617 -5.684404e-01 -0.044045398
## [192,]   1.27769586 -0.4528908326  0.1150534175  1.173032e-02 -0.010051253
## [193,]   1.09693599 -0.4344151638  0.2381189714 -4.626280e-02  0.021607927
## [194,]  -0.81285702 -0.8912956579 -0.1963626901  7.383901e-01  0.597568986
## [195,]   1.00169591 -0.2619137189  0.3502776810  1.257535e-01  0.033380504
## [196,]   0.45245343  0.9280037294 -0.5185901798 -1.246246e-01  0.129445254
## [197,]   0.08628883  2.7568111298 -1.8229643830 -1.018957e-01 -0.059879885
## [198,]  -0.39085008 -0.3955405972  0.1964547248  1.120201e-02 -0.014723123
## [199,]   0.66997842 -0.0262749566 -0.1984931057  1.164929e-01  0.283969333
## [200,]   1.02565202 -0.4494088678  0.2308137614 -1.343236e-01 -0.022683101
## [201,]  -2.23900996 -0.5878260801 -0.7085900734  8.764202e-02  0.116989345
## [202,]  -2.99546346 -0.6844705504 -0.6063795435  4.206181e-01 -0.406247403
## [203,]  -0.68180673  1.6877976045  1.1111432584 -1.448361e-01  0.296475108
## [204,]   1.10109815 -0.5880892539  0.1182040110  4.898085e-02 -0.075060624
## [205,]   0.89280368 -0.1557704566  0.2918836756  2.145287e-01  0.247566809
## [206,]  -2.04834810 -1.0164029887 -0.2749671288  1.925170e-01  0.277801549
## [207,]   1.22289397 -0.4091923864  0.1658758384 -1.619192e-02 -0.086383217
## [208,]   0.02999763 -0.4562055716 -0.3960906986  7.069393e-02 -0.444580597
## [209,]   0.29338844 -0.3614455997 -0.0080606821  1.020401e-01 -0.194049088
## [210,]  -2.07821189 -1.0624050684 -0.2629478297  9.111398e-02 -0.702586793
## [211,]   0.95666185  0.1415798527  0.4661520779  8.654914e-02 -0.108537036
## [212,]  -5.65091274 -0.5719339518 -0.7387671291 -1.300213e-01 -0.126122041
## [213,]   1.01303835 -0.0291142686  0.4447647467  1.647516e-01 -0.039979160
## [214,]  -0.07733767 -0.3524530076  0.1631543516 -1.007511e-01 -0.224364938
## [215,]  -0.54162222 -0.6955489007 -0.0163762810  1.424171e-01 -0.152658315
## [216,]  -1.23239191 -0.2683704471  0.2912940521 -1.525642e-02  0.112285888
## [217,]  -3.65784251 -1.5024946145 -0.4451166133  3.442908e-01  0.657875917
## [218,]   1.03509689  0.0266087310  0.1292185239  4.633317e-02 -0.017602064
## [219,]  -1.19058168  0.6205930559  1.2442387713  7.184164e-01  0.142727311
## [220,]   1.25137280 -0.2392367905 -0.0817948446  2.619077e-02 -0.024885647
## [221,]   1.16786662 -0.1694031479  0.1501129365  2.960327e-02 -0.038677735
## [222,]  -0.30619270 -0.8089351138  0.0668910915 -1.868201e-01  0.063360480
## [223,]   1.02353682  0.5442296394 -0.7992298261  8.139072e-02  0.023241419
## [224,]   0.64173440  0.4433723400 -0.3296613548  1.340806e-01  0.105076655
## [225,]   1.19242546 -0.3378506721  0.2671314257  4.137322e-02 -0.022546599
## [226,]   0.74927539 -0.3702922405  0.2832530799 -9.813612e-02  0.063127379
## [227,]  -0.04166179 -0.1845337776  0.1953124055 -4.971583e-03  0.146592921
## [228,]   1.03747427 -0.1018997011  0.0652443951 -9.734645e-02 -0.063282394
## [229,]   0.74782120 -0.6691384055 -0.0398167843  3.062108e-01 -0.753030645
## [230,]   0.82806814  0.5910908116 -0.5551384969 -1.856014e-02 -0.089465542
## [231,]   0.25762310  1.0470755800 -0.5119581753 -1.145021e-01  0.051283570
## [232,]   0.14712185 -0.2486236341  0.1632538632 -9.088454e-01 -0.116555921
## [233,]   0.92806057 -0.3530682004  0.3031763812  2.615664e-02  0.114450635
## [234,]   0.77748264 -0.4430065220  0.1067856518 -4.316804e-01  0.059574527
## [235,]   0.67882658  0.5685557802  0.1896331714  1.585129e-01  0.034903691
## [236,]   0.58424690 -0.3544175668  0.1247594862 -5.103974e-01 -0.111243449
## [237,]   1.07019195 -0.2560573276 -0.0902724213  6.404733e-02  0.048960534
## [238,]   0.93984852  0.4097679695 -0.1117504327 -2.455267e-01 -0.140479637
## [239,]   1.29676093 -0.3771593082  0.1253457821 -1.504406e-02 -0.080820647
## [240,]   0.65211081  0.6117600861 -0.0475416452  1.822848e-01 -0.037125264
## [241,]   0.35751675  1.5650061126 -0.8886851108  2.372639e-01  0.233027565
## [242,]   0.96409594 -0.0619058462  0.1362730091  2.831163e-02 -0.022388607
## [243,]   1.02852505  0.0209240042 -0.2246841232  1.443754e-01 -0.002387319
## [244,]   0.42242573 -0.0883244925  0.6300559875  1.449717e-01 -0.041947263
## [245,]  -0.37409228 -0.2051916783  0.3552773511 -7.683646e-02  0.167212011
## [246,]  -1.17838892 -0.5677000690  0.3926909992  7.040641e-01 -0.434158944
## [247,]   0.99935781 -0.2027092622  0.1142067686 -1.174565e-01 -0.067239648
## [248,]   1.26979462 -0.1376011824  0.0892026613  5.425859e-02 -0.100974997
## [249,]   0.74868436 -0.3609679907  0.3041702147 -4.226251e-01 -0.047178655
## [250,]   0.81396957  0.3749872762 -0.6333171467 -2.174539e-01 -0.138534187
## [251,]   1.04468274 -0.1831538258  0.1467280904 -7.118688e-02 -0.037489850
## [252,]  -5.00768849  0.2866944486 -0.4530671996  4.696430e-01 -0.518324418
## [253,]   0.74545878  0.8487520877 -0.5316791722  2.080796e-01  0.131960206
## [254,]  -0.38605647 -0.3822564073  0.3596740591 -1.697875e-01  1.053331483
## [255,]  -0.70708219  0.9391578638  0.4174818883 -1.347493e+00 -0.181354924
## [256,]   1.18411490  0.0030724566 -0.1056092382  8.228318e-02 -0.039791764
## [257,]   0.63210547 -0.4617583277  0.2382291091 -3.355262e-01  0.201599925
## [258,]   0.60371331  0.1584360306 -0.4021340143  2.429649e-01 -0.537359370
## [259,]   0.51724649  1.0841565656  0.0813394709  3.147487e-02 -0.197104415
## [260,]   0.38236102 -0.0600224883 -0.0825430899 -1.448918e-01  0.252324354
## [261,]   0.77157492 -0.4143575173  0.3222401594 -3.760689e-01 -0.093166151
## [262,]   1.16886889  0.4671003805 -0.6890125078 -7.043557e-03 -0.075260316
## [263,]   1.08603962 -0.3224084602  0.2292812684 -5.347571e-03 -0.065522333
## [264,]   0.50559973 -0.1198310239 -0.4845642221  3.683120e-01 -0.046730481
## [265,]  -1.05801199 -0.7327306364  0.2015378961 -2.695094e-02  0.128243055
## [266,]  -1.65734964  1.7937030127 -0.3176590716 -1.632266e+00  0.531331804
## [267,]  -1.47739059 -0.1772552412  0.1448843315  2.739655e-01  0.750619450
## [268,]   0.72868453  0.7388604273  0.4633191765  4.314102e-01 -0.139527389
## [269,]  -1.21350291 -0.8331254104 -0.1733097803  2.719002e-01  0.427226378
## [270,]   1.23813362 -0.2040031259 -0.1028955543  5.837019e-02 -0.082046653
## [271,]   1.19514203  0.2171972169 -0.5560636672 -3.087829e-02 -0.091495871
## [272,]   0.78067858 -0.0285014779  0.4761824614 -3.323474e-01 -0.080771179
## [273,]   0.26602762 -0.2600598349  0.4141737602 -5.980265e-01  0.329535881
## [274,]   0.86878444  0.5324167641 -0.0225250867 -4.330202e-02 -0.111256960
## [275,]   0.97282972 -0.2621784812  0.3694564929  4.112342e-02 -0.114859043
## [276,]   1.22069804 -0.3548028456  0.2178276618 -1.359238e-01 -0.121674632
## [277,]   0.38108645  0.5359681743  0.1031818081  1.588676e-01  0.228136410
## [278,]   1.07846333  1.8653583443 -2.2187714566  1.341660e-01 -0.237361123
## [279,]   0.87750350  0.5586473422 -0.2976317207  3.982789e-02 -0.030181815
## [280,]  -0.22439955 -0.2780541521  0.2576621230  6.954580e-02  0.028826443
## [281,]   0.92072808 -0.1969571181  0.3540777128 -1.174575e-01  0.008145334
## [282,]   0.04172049 -0.0827385077  0.4799604369 -1.985353e-01 -0.063973268
## [283,]   0.56179348  0.5294798027 -0.3505102112 -3.311987e-02 -0.019932544
## [284,]   0.77559110  1.2246245312 -0.9328150131 -7.866405e-02 -0.107268673
## [285,]  -0.05666773  1.0332866463 -0.6082059064  3.097958e-01  0.613305200
## [286,]   1.07514112 -0.4990147752  0.0360851368  6.764338e-02  0.101806296
## [287,]   0.99534417 -0.3724699669 -0.0025361652 -1.141551e-01 -0.206668238
## [288,]   0.87483219  0.8238467598 -0.7660903317  6.233610e-02 -0.026198954
## [289,]   1.19971862 -0.4370617387  0.1507336728  2.377307e-02 -0.080498744
## [290,]   1.33657531 -0.3792644504  0.0403934684 -1.991985e-02 -0.078747463
## [291,]   0.83674885 -0.2326950986  0.4778908332  7.063094e-02 -0.094983491
## [292,]   0.85316130 -0.0776399639  0.0255349598 -1.724166e-01  0.065639153
## [293,]   0.69360374  0.1417127149 -0.1231390079 -7.944642e-03  0.043145957
## [294,]  -0.93965965 -0.6554126047  0.0144458692 -3.368204e-01 -0.092794885
## [295,]   0.59455930 -0.1573054188  0.4481372130  2.453625e-01  0.214344165
## [296,]   0.66171399 -0.6451195060  0.1053069563  1.281564e-01 -0.038034651
## [297,]   0.90049568 -0.0190226696 -0.0533317316  1.344791e-01  0.026534235
## [298,]   0.25180413 -0.5274174486 -0.0489267035  1.892655e-01 -0.140887343
## [299,]  -0.16562608 -0.5647513335  0.0893655028  2.460353e-01 -0.051401842
## [300,]   1.15462330 -0.5205877239  0.2356021757  9.127424e-05  0.001409648
## [301,]   0.06749116 -0.1726847894  0.4762957660 -8.485776e-02 -0.093726153
## [302,]  -1.87238584 -0.9062380384 -0.4427004461 -1.810361e-01  0.108661941
## [303,]  -0.36075328 -0.8370400050  0.0032583493  2.182948e-01 -0.296139923
## [304,]  -0.89344120 -1.2389830186 -0.3587903929  7.500908e-01 -0.514394929
## [305,]  -2.24170924 -0.9151722866  0.0047365098  1.077483e+00 -0.014103893
## [306,]  -0.57018410 -0.5842186912  0.0578018787 -8.680445e-01 -0.071166812
## [307,]  -1.88935546 -0.5541561209 -0.0993321247 -2.146956e-02  0.333094843
## [308,]   0.92559692 -0.2371239152  0.2679024918 -5.256295e-02  0.020162445
## [309,]   1.05503352 -0.4215247836  0.2968103229  5.963136e-02  0.065581698
## [310,]  -1.82444685 -0.4800857869  0.0137381216 -1.292307e+00 -0.197719739
## [311,]   0.91380091  1.4544571140 -1.3567395155  1.620224e-01 -0.067659925
## [312,]   0.64646544 -0.2336199078 -0.2728305098  5.699709e-02  0.444370877
## [313,]  -2.05651935 -1.5961639143 -0.8061189963  1.441392e+00 -1.124041662
## [314,]   1.10515579  0.0942827022 -0.3658363964  4.389359e-02  0.019092121
## [315,]   0.58629339 -0.2366852388  0.1994980699  2.435903e-01  0.306900770
## [316,]  -1.18632311  0.1134601388  0.8352376886 -6.227835e-01  0.062245747
## [317,]   1.04565960  0.0243938808  0.0831196910  4.934935e-02  0.003501565
## [318,]   0.55882703 -0.1724359049  0.4057778341  8.754597e-02  0.179102456
## [319,]   0.88204365 -0.3180530565 -0.0985570540 -1.318735e-01  0.041084475
## [320,]  -3.11235419 -0.6616337617  0.0320866751 -1.164397e+00 -0.730470849
## [321,]   0.88439078 -0.3152197306  0.3659850754 -2.408060e-01 -0.013520147
## [322,]   0.80386112 -0.0072506990  0.0513815263  1.045981e-01  0.204073016
## [323,]   0.92745036 -0.1201143087 -0.3393779899  1.744727e-01 -0.088752154
## [324,]   0.37271862 -0.5907448216  0.0313892316  4.454996e-01  0.516413252
## [325,]   0.85971976  0.0136909553  0.1573108564 -1.846572e-01  0.003240288
## [326,]  -1.78946833  9.4426161661 -7.3561656089 -1.262653e-01  0.172452266
## [327,]   1.05267151  0.0916580173 -0.0880866187  2.103203e-03 -0.098249788
## [328,]   1.17723864 -0.4219320559  0.2890068608  1.941328e-03 -0.008117440
## [329,]   0.81408444  0.8645867977 -0.5709617552  1.088298e-01  0.029775378
## [330,]   0.85138951  0.2466297340 -0.3962137780  1.314342e-01  0.121544020
## [331,]   0.81990469  0.1028458245 -0.0887119701  1.122326e-01  0.204217975
## [332,]  -2.55569469 -0.9119772593 -0.2422695809  1.565106e-02  0.445203963
## [333,]   0.81764691  0.3357835077  0.5424978555 -2.891576e-03 -0.118900424
## [334,]  -7.61379702 -3.4878261273 -1.8570054614  4.487063e+00 -0.492430881
## [335,]   0.73733540  1.8203153674 -0.6665945815  4.988941e-01 -0.104095182
## [336,]  -0.43016311 -0.2108130517  0.3183683323  1.198782e-01  0.026361034
## [337,]   1.12215088 -0.3190418064  0.3242381916 -4.171648e-02 -0.053885459
## [338,]   0.95236916  0.7486749232 -0.7833034255  1.236485e-01 -0.040856249
## [339,]   0.77302224  1.6893212630 -1.9971202384  3.868789e-01  0.331097800
## [340,]   0.67925139  1.1382025886 -0.7816151404  3.759789e-01  0.111049057
## [341,]  -0.44952190 -0.7286057941  0.1357307410  5.248944e-01 -0.468668348
## [342,]  -0.49874907 -0.3767392711  0.3492630012  3.240041e-01 -0.081203551
## [343,]  -0.03297929 -0.5029489774  0.3096893528  1.177555e-02 -0.379628062
## [344,]  -2.53250139 -1.5660071985 -0.8480530559  1.184938e+00 -0.359835221
## [345,]   1.13340753 -0.1952182547 -0.0133121117 -1.458200e-02 -0.026484205
## [346,]   0.22596844 -0.7694471361  0.0206476758  2.730768e-01 -0.041278788
## [347,]  -0.94277386 -0.4648303557 -0.2772970552  3.357660e-01  0.052682251
## [348,]  -0.52623469 -0.2992166497 -0.1906294560  5.170232e-02  0.090517992
## [349,]   0.89883641 -0.3013837867  0.1566870505 -4.785936e-02 -0.155021430
## [350,]  -2.40481023 -0.9960767917 -0.5310822389 -4.374715e-02 -0.394974382
## [351,]   1.08068712 -0.1237118941  0.1927739106  6.405186e-02 -0.016769761
## [352,]  -2.45061408 -0.5584735441  0.0419149034  8.628946e-01 -0.367013462
## [353,]   1.19422964 -0.4293999671  0.1558240037 -5.857045e-02 -0.012704664
## [354,]  -1.46109306 -1.0443346120 -0.0859166808  7.205129e-01  0.203389284
## [355,]   0.29654054  0.8630742744 -0.1383954212 -3.401633e-01 -0.240078342
## [356,]   1.19246382 -0.5482961618  0.2104436785 -7.319833e-03  0.017614488
## [357,]   1.30670647 -0.0029419227 -0.0920076981  6.454974e-02 -0.118117924
## [358,]  -0.84837304 -1.2653251323 -0.3054295861  1.059554e+00  0.619631964
## [359,]  -0.53430822  1.4509195863  0.4951650461 -1.488780e+00 -0.307004553
## [360,]   0.74548879 -0.3141877231  0.4084485713 -5.018286e-01 -0.030554517
## [361,]   0.95060230 -0.1063642743 -0.0303243494 -1.610490e-01 -0.059279836
## [362,]   1.24298882 -0.3289021623  0.1503307078  8.015338e-03 -0.078577675
## [363,]   1.04927604 -0.3656586146  0.3065814927 -2.120530e-02  0.028795306
## [364,]   0.87486904 -0.6155984555  0.1869141366  1.449102e-01  0.031142672
## [365,]   1.13722957 -0.3566829731  0.1603429922  3.141357e-02 -0.081879125
## [366,]  -0.34134077  0.0528651642  0.5204387607  2.484323e-01 -0.266636410
## [367,]   1.06478454 -0.3160073629  0.1713890889 -1.369749e-01 -0.037004496
## [368,]   1.23457189 -0.3020715155  0.1031540306 -3.290657e-02 -0.118323974
## [369,]   1.09202865 -0.1860571487  0.0523766298  1.397055e-02  0.035019264
## [370,]   1.29790056 -0.3646317914  0.1456950323  1.026699e-02 -0.070216959
## [371,]   0.54728205  0.0660108492  0.5275880023  4.670435e-03  0.109653457
## [372,]   0.92861428  0.7341864175 -0.7960212484  5.201769e-02 -0.132267223
## [373,]   0.55848361  0.6329891063  1.2548922421  1.947481e-01 -0.193946445
## [374,]  -0.01036762  0.1984867185  0.6528332213  2.705561e-02  0.057534446
## [375,]   1.02837629 -0.2211011595  0.1777392160 -1.044276e-01 -0.058081877
## [376,]   1.15932849 -0.5015726865  0.1543070714 -9.802522e-02 -0.093532531
## [377,]  -0.77356526  0.1996188872 -0.5105311814  8.662076e-03  0.146226030
## [378,]   0.88358086 -0.1532556029  0.3813297561 -1.293612e-01  0.029117565
## [379,]   0.93923945 -0.2746083703  0.4739350118 -1.933370e-01 -0.016908645
## [380,]   0.27600519 -0.6575609068  0.1558497541 -1.804023e-01  0.539501791
## [381,]   1.07810889 -0.0128717819 -0.3024832323  5.457804e-02 -0.056683715
## [382,]   0.81131596  1.0058196043 -1.0577260590 -3.067384e-01 -0.107566207
## [383,]  -0.12863861  0.3117748537  0.4582050708 -9.939952e-02  0.162220332
## [384,]   0.98212572  0.0222401601 -0.3036920467  4.719205e-02  0.066127080
## [385,]  -1.64808006  1.1586559064  0.9605663032 -1.324026e+00  0.742990749
## [386,]   1.10233193  0.0088755009  0.0972514015  8.876743e-02 -0.053949151
## [387,]   0.82259230 -0.0935972530  0.1765052575 -1.786855e-01  0.008277633
## [388,]   1.04129188 -0.0912372095  0.1742296693 -3.926493e-02 -0.062097721
## [389,]   1.19768522 -0.2641713568  0.0789849464 -1.220946e-03 -0.064952858
## [390,]   1.09437876 -0.0030619385 -0.0478148524 -2.252481e-02 -0.068766279
## [391,]   1.06891237  0.4179833336 -0.3424848203  7.987405e-02 -0.108186282
## [392,]   0.88438236 -0.0417631467  0.5367800244 -3.089990e-02 -0.009649391
## [393,]   0.79981986 -0.3397531358  0.2968846699 -2.819700e-01  0.110441519
## [394,]   0.48759544  0.8695421826 -0.8090023384 -4.435117e-01  0.028695796
## [395,]   1.07628493 -0.3243979663  0.1054144579  6.200560e-02  0.097367055
## [396,]   1.08292394 -0.1408151659 -0.1508761886 -5.685268e-03 -0.156053509
## [397,]  -0.65441107  0.1365619541  0.2609186633 -5.374683e-01 -0.017928094
## [398,]   1.06672699  0.5739678319 -0.5833083159 -5.032264e-03 -0.068046024
## [399,]   1.21812567  0.2573167088 -0.4850298560 -3.179681e-02 -0.108576616
## [400,]   1.20418087 -0.2977446541  0.0719496515  3.635687e-02 -0.118696408
## [401,]   1.12755720  0.1486469749 -0.0539299714  7.907698e-02 -0.080788486
## [402,]   0.78619937  1.7607701632 -1.2401567867  8.773626e-02 -0.092231125
## [403,]   0.70963764 -0.4824173163  0.2787551961 -3.455904e-01  0.247948235
## [404,]   0.21181784 -0.4378501159  0.3382349083 -1.023084e+00  0.087221718
## [405,]   0.65039342  0.1682494910 -0.2479710243 -2.358100e-01 -0.038949793
## [406,]   1.13695208 -0.2329491833  0.0020048404  5.289853e-03 -0.124123853
## [407,]   0.43799628  0.9861577681 -1.0141918729 -1.341328e-01  0.017341293
## [408,]  -1.67259278 -0.5997607604 -0.4539003847 -1.927750e-01  0.088799367
## [409,]   0.36550163 -0.4654167058 -0.0653570248  4.368427e-03 -0.044121872
## [410,]   0.05904374  0.7407264885  0.9812353376  5.321543e-01 -0.116912163
## [411,]   0.58114647 -0.1053616044  0.3728519656  2.555079e-01 -0.091531240
## [412,]   0.54871526  0.5993113197  1.0280690648  2.474061e-01 -0.033336374
## [413,]   0.02754893 -0.8683954018  0.0009452655  2.004207e-01  0.396172149
## [414,]   0.18022987  2.4627986053 -1.8610262286  1.696222e-01  0.081699407
## [415,]   0.84472130  0.2166544351 -0.5858918678  3.730761e-02 -0.052819470
## [416,]  -0.15011103 -0.1654789686  0.2521128931  6.515206e-02 -0.052293459
## [417,]  -0.94319868 -0.6282524920  0.0694434201 -2.856556e-01 -0.328750555
## [418,]  -0.17681577 -0.5846549679  0.2174968459  9.846607e-02  0.179411157
## [419,]  -1.21247875 -0.9451190928 -0.0111536007  2.085788e-01  0.281727286
## [420,]   0.67045226 -0.2169645295  0.4594481571 -7.930226e-02 -0.225166310
## [421,]  -0.70505273 -0.7893865579  0.1792825081  4.685864e-01 -0.138527213
## [422,]  -0.06490484 -0.3007384881  0.3109499418  1.898877e-01  0.016876618
## [423,]   0.82591686 -0.2892677213  0.3292781858  1.754135e-01  0.035366768
## [424,]   0.57180936 -0.3995984651  0.1544486982 -6.623976e-02 -0.049472294
## [425,]   0.04046836 -0.7367264203 -0.0847164943  3.219454e-01  0.343336774
## [426,]   0.76883248  2.0500342258 -1.5657601158  1.670196e-01 -0.067827419
## [427,]  -0.93848842 -0.0821362098 -0.0534415939  1.076078e-02  0.138959378
## [428,]  -0.43132555  2.0067711242 -1.5734003459 -1.398859e+00  0.039329073
## [429,]   0.51934102 -0.2273851246 -0.0315692426 -4.106207e-01  0.096672075
## [430,]   0.83217183 -0.0517546591  0.7913966759  1.911758e-01  0.080207639
## [431,]  -0.12732308 -0.2510251070  0.4661498794  3.030175e-01  1.035711609
## [432,]   0.28430937  1.6278170123 -1.4322862099 -6.732602e-02 -0.051096480
## [433,]   0.83664364 -0.5884685158  0.1925679473  1.462679e-01  0.052584928
## [434,]   0.89763536 -0.0286593561  0.3618008079 -1.269600e-01 -0.105069502
## [435,]   0.27267232 -0.4987640539  0.1838051451  7.266804e-02  0.119401988
## [436,]  -0.78171970  1.7262064236 -1.2339946527 -4.534560e-01  0.892440952
## [437,]   1.00383404  0.6000966110  0.1372499975  1.617472e-01 -0.153667550
## [438,]  -3.47543102 -1.2015869428 -0.1938524404  5.134742e-01 -0.065875377
## [439,]   0.91187529  0.0286815529  0.5761825595  9.421507e-02 -0.030771798
## [440,]   1.06427400 -0.6008476585  0.2126003922 -8.899895e-02  0.011009682
plot(wholesale_pca)

#get the original value of the data based on PCA
center <- wholesale_pca$center
scale <- wholesale_pca$scale
new_wholesale <- as.matrix(wholesale[,-1])
new_wholesale
##         Fresh  Milk Grocery Frozen Detergents_Paper Delicassen
##   [1,]  12669  9656    7561    214             2674       1338
##   [2,]   7057  9810    9568   1762             3293       1776
##   [3,]   6353  8808    7684   2405             3516       7844
##   [4,]  13265  1196    4221   6404              507       1788
##   [5,]  22615  5410    7198   3915             1777       5185
##   [6,]   9413  8259    5126    666             1795       1451
##   [7,]  12126  3199    6975    480             3140        545
##   [8,]   7579  4956    9426   1669             3321       2566
##   [9,]   5963  3648    6192    425             1716        750
##  [10,]   6006 11093   18881   1159             7425       2098
##  [11,]   3366  5403   12974   4400             5977       1744
##  [12,]  13146  1124    4523   1420              549        497
##  [13,]  31714 12319   11757    287             3881       2931
##  [14,]  21217  6208   14982   3095             6707        602
##  [15,]  24653  9465   12091    294             5058       2168
##  [16,]  10253  1114    3821    397              964        412
##  [17,]   1020  8816   12121    134             4508       1080
##  [18,]   5876  6157    2933    839              370       4478
##  [19,]  18601  6327   10099   2205             2767       3181
##  [20,]   7780  2495    9464    669             2518        501
##  [21,]  17546  4519    4602   1066             2259       2124
##  [22,]   5567   871    2010   3383              375        569
##  [23,]  31276  1917    4469   9408             2381       4334
##  [24,]  26373 36423   22019   5154             4337      16523
##  [25,]  22647  9776   13792   2915             4482       5778
##  [26,]  16165  4230    7595    201             4003         57
##  [27,]   9898   961    2861   3151              242        833
##  [28,]  14276   803    3045    485              100        518
##  [29,]   4113 20484   25957   1158             8604       5206
##  [30,]  43088  2100    2609   1200             1107        823
##  [31,]  18815  3610   11107   1148             2134       2963
##  [32,]   2612  4339    3133   2088              820        985
##  [33,]  21632  1318    2886    266              918        405
##  [34,]  29729  4786    7326   6130              361       1083
##  [35,]   1502  1979    2262    425              483        395
##  [36,]    688  5491   11091    833             4239        436
##  [37,]  29955  4362    5428   1729              862       4626
##  [38,]  15168 10556   12477   1920             6506        714
##  [39,]   4591 15729   16709     33             6956        433
##  [40,]  56159   555     902  10002              212       2916
##  [41,]  24025  4332    4757   9510             1145       5864
##  [42,]  19176  3065    5956   2033             2575       2802
##  [43,]  10850  7555   14961    188             6899         46
##  [44,]    630 11095   23998    787             9529         72
##  [45,]   9670  7027   10471    541             4618         65
##  [46,]   5181 22044   21531   1740             7353       4985
##  [47,]   3103 14069   21955   1668             6792       1452
##  [48,]  44466 54259   55571   7782            24171       6465
##  [49,]  11519  6152   10868    584             5121       1476
##  [50,]   4967 21412   28921   1798            13583       1163
##  [51,]   6269  1095    1980   3860              609       2162
##  [52,]   3347  4051    6996    239             1538        301
##  [53,]  40721  3916    5876    532             2587       1278
##  [54,]    491 10473   11532    744             5611        224
##  [55,]  27329  1449    1947   2436              204       1333
##  [56,]   5264  3683    5005   1057             2024       1130
##  [57,]   4098 29892   26866   2616            17740       1340
##  [58,]   5417  9933   10487     38             7572       1282
##  [59,]  13779  1970    1648    596              227        436
##  [60,]   6137  5360    8040    129             3084       1603
##  [61,]   8590  3045    7854     96             4095        225
##  [62,]  35942 38369   59598   3254            26701       2017
##  [63,]   7823  6245    6544   4154             4074        964
##  [64,]   9396 11601   15775   2896             7677       1295
##  [65,]   4760  1227    3250   3724             1247       1145
##  [66,]     85 20959   45828     36            24231       1423
##  [67,]      9  1534    7417    175             3468         27
##  [68,]  19913  6759   13462   1256             5141        834
##  [69,]   2446  7260    3993   5870              788       3095
##  [70,]   8352  2820    1293    779              656        144
##  [71,]  16705  2037    3202  10643              116       1365
##  [72,]  18291  1266   21042   5373             4173      14472
##  [73,]   4420  5139    2661   8872             1321        181
##  [74,]  19899  5332    8713   8132              764        648
##  [75,]   8190  6343    9794   1285             1901       1780
##  [76,]  20398  1137       3   4407                3        975
##  [77,]    717  3587    6532   7530              529        894
##  [78,]  12205 12697   28540    869            12034       1009
##  [79,]  10766  1175    2067   2096              301        167
##  [80,]   1640  3259    3655    868             1202       1653
##  [81,]   7005   829    3009    430              610        529
##  [82,]    219  9540   14403    283             7818        156
##  [83,]  10362  9232   11009    737             3537       2342
##  [84,]  20874  1563    1783   2320              550        772
##  [85,]  11867  3327    4814   1178             3837        120
##  [86,]  16117 46197   92780   1026            40827       2944
##  [87,]  22925 73498   32114    987            20070        903
##  [88,]  43265  5025    8117   6312             1579      14351
##  [89,]   7864   542    4042   9735              165         46
##  [90,]  24904  3836    5330   3443              454       3178
##  [91,]  11405   596    1638   3347               69        360
##  [92,]  12754  2762    2530   8693              627       1117
##  [93,]   9198 27472   32034   3232            18906       5130
##  [94,]  11314  3090    2062  35009               71       2698
##  [95,]   5626 12220   11323    206             5038        244
##  [96,]      3  2920    6252    440              223        709
##  [97,]     23  2616    8118    145             3874        217
##  [98,]    403   254     610    774               54         63
##  [99,]    503   112     778    895               56        132
## [100,]   9658  2182    1909   5639              215        323
## [101,]  11594  7779   12144   3252             8035       3029
## [102,]   1420 10810   16267   1593             6766       1838
## [103,]   2932  6459    7677   2561             4573       1386
## [104,]  56082  3504    8906  18028             1480       2498
## [105,]  14100  2132    3445   1336             1491        548
## [106,]  15587  1014    3970    910              139       1378
## [107,]   1454  6337   10704    133             6830       1831
## [108,]   8797 10646   14886   2471             8969       1438
## [109,]   1531  8397    6981    247             2505       1236
## [110,]   1406 16729   28986    673              836          3
## [111,]  11818  1648    1694   2276              169       1647
## [112,]  12579 11114   17569    805             6457       1519
## [113,]  19046  2770    2469   8853              483       2708
## [114,]  14438  2295    1733   3220              585       1561
## [115,]  18044  1080    2000   2555              118       1266
## [116,]  11134   793    2988   2715              276        610
## [117,]  11173  2521    3355   1517              310        222
## [118,]   6990  3880    5380   1647              319       1160
## [119,]  20049  1891    2362   5343              411        933
## [120,]   8258  2344    2147   3896              266        635
## [121,]  17160  1200    3412   2417              174       1136
## [122,]   4020  3234    1498   2395              264        255
## [123,]  12212   201     245   1991               25        860
## [124,]  11170 10769    8814   2194             1976        143
## [125,]  36050  1642    2961   4787              500       1621
## [126,]  76237  3473    7102  16538              778        918
## [127,]  19219  1840    1658   8195              349        483
## [128,]  21465  7243   10685    880             2386       2749
## [129,]    140  8847    3823    142             1062          3
## [130,]  42312   926    1510   1718              410       1819
## [131,]   7149  2428     699   6316              395        911
## [132,]   2101   589     314    346               70        310
## [133,]  14903  2032    2479    576              955        328
## [134,]   9434  1042    1235    436              256        396
## [135,]   7388  1882    2174    720               47        537
## [136,]   6300  1289    2591   1170              199        326
## [137,]   4625  8579    7030   4575             2447       1542
## [138,]   3087  8080    8282    661              721         36
## [139,]  13537  4257    5034    155              249       3271
## [140,]   5387  4979    3343    825              637        929
## [141,]  17623  4280    7305   2279              960       2616
## [142,]  30379 13252    5189    321               51       1450
## [143,]  37036  7152    8253   2995               20          3
## [144,]  10405  1596    1096   8425              399        318
## [145,]  18827  3677    1988    118              516        201
## [146,]  22039  8384   34792     42            12591       4430
## [147,]   7769  1936    2177    926               73        520
## [148,]   9203  3373    2707   1286             1082        526
## [149,]   5924   584     542   4052              283        434
## [150,]  31812  1433    1651    800              113       1440
## [151,]  16225  1825    1765    853              170       1067
## [152,]   1289  3328    2022    531              255       1774
## [153,]  18840  1371    3135   3001              352        184
## [154,]   3463  9250    2368    779              302       1627
## [155,]    622    55     137     75                7          8
## [156,]   1989 10690   19460    233            11577       2153
## [157,]   3830  5291   14855    317             6694       3182
## [158,]  17773  1366    2474   3378              811        418
## [159,]   2861  6570    9618    930             4004       1682
## [160,]    355  7704   14682    398             8077        303
## [161,]   1725  3651   12822    824             4424       2157
## [162,]  12434   540     283   1092                3       2233
## [163,]  15177  2024    3810   2665              232        610
## [164,]   5531 15726   26870   2367            13726        446
## [165,]   5224  7603    8584   2540             3674        238
## [166,]  15615 12653   19858   4425             7108       2379
## [167,]   4822  6721    9170    993             4973       3637
## [168,]   2926  3195    3268    405             1680        693
## [169,]   5809   735     803   1393               79        429
## [170,]   5414   717    2155   2399               69        750
## [171,]    260  8675   13430   1116             7015        323
## [172,]    200 25862   19816    651             8773       6250
## [173,]    955  5479    6536    333             2840        707
## [174,]    514  7677   19805    937             9836        716
## [175,]    286  1208    5241   2515              153       1442
## [176,]   2343  7845   11874     52             4196       1697
## [177,]  45640  6958    6536   7368             1532        230
## [178,]  12759  7330    4533   1752               20       2631
## [179,]  11002  7075    4945   1152              120        395
## [180,]   3157  4888    2500   4477              273       2165
## [181,]  12356  6036    8887    402             1382       2794
## [182,] 112151 29627   18148  16745             4948       8550
## [183,]    694  8533   10518    443             6907        156
## [184,]  36847 43950   20170  36534              239      47943
## [185,]    327   918    4710     74              334         11
## [186,]   8170  6448    1139   2181               58        247
## [187,]   3009   521     854   3470              949        727
## [188,]   2438  8002    9819   6269             3459          3
## [189,]   8040  7639   11687   2758             6839        404
## [190,]    834 11577   11522    275             4027       1856
## [191,]  16936  6250    1981   7332              118         64
## [192,]  13624   295    1381    890               43         84
## [193,]   5509  1461    2251    547              187        409
## [194,]    180  3485   20292    959             5618        666
## [195,]   7107  1012    2974    806              355       1142
## [196,]  17023  5139    5230   7888              330       1755
## [197,]  30624  7209    4897  18711              763       2876
## [198,]   2427  7097   10391   1127             4314       1468
## [199,]  11686  2154    6824   3527              592        697
## [200,]   9670  2280    2112    520              402        347
## [201,]   3067 13240   23127   3941             9959        731
## [202,]   4484 14399   24708   3549            14235       1681
## [203,]  25203 11487    9490   5065              284       6854
## [204,]    583   685    2216    469              954         18
## [205,]   1956   891    5226   1383                5       1328
## [206,]   1107 11711   23596    955             9265        710
## [207,]   6373   780     950    878              288        285
## [208,]   2541  4737    6089   2946             5316        120
## [209,]   1537  3748    5838   1859             3381        806
## [210,]   5550 12729   16767    864            12420        797
## [211,]  18567  1895    1393   1801              244       2100
## [212,]  12119 28326   39694   4736            19410       2870
## [213,]   7291  1012    2062   1291              240       1775
## [214,]   3317  6602    6861   1329             3961       1215
## [215,]   2362  6551   11364    913             5957        791
## [216,]   2806 10765   15538   1374             5828       2388
## [217,]   2532 16599   36486    179            13308        674
## [218,]  18044  1475    2046   2532              130       1158
## [219,]     18  7504   15205   1285             4797       6372
## [220,]   4155   367    1390   2306               86        130
## [221,]  14755   899    1382   1765               56        749
## [222,]   5396  7503   10646     91             4167        239
## [223,]   5041  1115    2856   7496              256        375
## [224,]   2790  2527    5265   5612              788       1360
## [225,]   7274   659    1499    784               70        659
## [226,]  12680  3243    4157    660              761        786
## [227,]  20782  5921    9212   1759             2568       1553
## [228,]   4042  2204    1563   2286              263        689
## [229,]   1869   577     572    950             4762        203
## [230,]   8656  2746    2501   6845              694        980
## [231,]  11072  5989    5615   8321              955       2137
## [232,]   2344 10678    3828   1439             1566        490
## [233,]  25962  1780    3838    638              284        834
## [234,]    964  4984    3316    937              409          7
## [235,]  15603  2703    3833   4260              325       2563
## [236,]   1838  6380    2824   1218             1216        295
## [237,]   8635   820    3047   2312              415        225
## [238,]  18692  3838     593   4634               28       1215
## [239,]   7363   475     585   1112               72        216
## [240,]  47493  2567    3779   5243              828       2253
## [241,]  22096  3575    7041  11422              343       2564
## [242,]  24929  1801    2475   2216              412       1047
## [243,]  18226   659    2914   3752              586        578
## [244,]  11210  3576    5119    561             1682       2398
## [245,]   6202  7775   10817   1183             3143       1970
## [246,]   3062  6154   13916    230             8933       2784
## [247,]   8885  2428    1777   1777              430        610
## [248,]  13569   346     489   2077               44        659
## [249,]  15671  5279    2406    559              562        572
## [250,]   8040  3795    2070   6340              918        291
## [251,]   3191  1993    1799   1730              234        710
## [252,]   6134 23133   33586   6746            18594       5121
## [253,]   6623  1860    4740   7683              205       1693
## [254,]  29526  7961   16966    432              363       1391
## [255,]  10379 17972    4748   4686             1547       3265
## [256,]  31614   489    1495   3242              111        615
## [257,]  11092  5008    5249    453              392        373
## [258,]   8475  1931    1883   5004             3593        987
## [259,]  56083  4563    2124   6422              730       3321
## [260,]  53205  4959    7336   3012              967        818
## [261,]   9193  4885    2157    327              780        548
## [262,]   7858  1110    1094   6818               49        287
## [263,]  23257  1372    1677    982              429        655
## [264,]   2153  1115    6684   4324             2894        411
## [265,]   1073  9679   15445     61             5980       1265
## [266,]   5909 23527   13699  10155              830       3636
## [267,]    572  9763   22182   2221             4882       2563
## [268,]  20893  1222    2576   3975              737       3628
## [269,]  11908  8053   19847   1069             6374        698
## [270,]  15218   258    1138   2516              333        204
## [271,]   4720  1032     975   5500              197         56
## [272,]   2083  5007    1563   1120              147       1550
## [273,]    514  8323    6869    529               93       1040
## [274,]  36817  3045    1493   4802              210       1824
## [275,]    894  1703    1841    744              759       1153
## [276,]    680  1610     223    862               96        379
## [277,]  27901  3749    6964   4479              603       2503
## [278,]   9061   829     683  16919              621        139
## [279,]  11693  2317    2543   5845              274       1409
## [280,]  17360  6200    9694   1293             3620       1721
## [281,]   3366  2884    2431    977              167       1104
## [282,]  12238  7108    6235   1093             2328       2079
## [283,]  49063  3965    4252   5970             1041       1404
## [284,]  25767  3613    2013  10303              314       1384
## [285,]  68951  4411   12609   8692              751       2406
## [286,]  40254   640    3600   1042              436         18
## [287,]   7149  2247    1242   1619             1226        128
## [288,]  15354  2102    2828   8366              386       1027
## [289,]  16260   594    1296    848              445        258
## [290,]  42786   286     471   1388               32         22
## [291,]   2708  2160    2642    502              965       1522
## [292,]   6022  3354    3261   2507              212        686
## [293,]   2838  3086    4329   3838              825       1060
## [294,]   3996 11103   12469    902             5952        741
## [295,]  21273  2013    6550    909              811       1854
## [296,]   7588  1897    5234    417             2208        254
## [297,]  19087  1304    3643   3045              710        898
## [298,]   8090  3199    6986   1455             3712        531
## [299,]   6758  4560    9965    934             4538       1037
## [300,]    444   879    2060    264              290        259
## [301,]  16448  6243    6360    824             2662       2005
## [302,]   5283 13316   20399   1809             8752        172
## [303,]   2886  5302    9785    364             6236        555
## [304,]   2599  3688   13829    492            10069         59
## [305,]    161  7460   24773    617            11783       2410
## [306,]    243 12939    8852    799             3909        211
## [307,]   6468 12867   21570   1840             7558       1543
## [308,]  17327  2374    2842   1149              351        925
## [309,]   6987  1020    3007    416              257        656
## [310,]    918 20655   13567   1465             6846        806
## [311,]   7034  1492    2405  12569              299       1117
## [312,]  29635  2335    8280   3046              371        117
## [313,]   2137  3737   19172   1274            17120        142
## [314,]   9784   925    2405   4447              183        297
## [315,]  10617  1795    7647   1483              857       1233
## [316,]   1479 14982   11924    662             3891       3508
## [317,]   7127  1375    2201   2679               83       1059
## [318,]   1182  3088    6114    978              821       1637
## [319,]  11800  2713    3558   2121              706         51
## [320,]   9759 25071   17645   1128            12408       1625
## [321,]   1774  3696    2280    514              275        834
## [322,]   9155  1897    5167   2714              228       1113
## [323,]  15881   713    3315   3703             1470        229
## [324,]  13360   944   11593    915             1679        573
## [325,]  25977  3587    2464   2369              140       1092
## [326,]  32717 16784   13626  60869             1272       5609
## [327,]   4414  1610    1431   3498              387        834
## [328,]    542   899    1664    414               88        522
## [329,]  16933  2209    3389   7849              210       1534
## [330,]   5113  1486    4583   5127              492        739
## [331,]   9790  1786    5109   3570              182       1043
## [332,]  11223 14881   26839   1234             9606       1102
## [333,]  22321  3216    1447   2208              178       2602
## [334,]   8565  4980   67298    131            38102       1215
## [335,]  16823   928    2743  11559              332       3486
## [336,]  27082  6817   10790   1365             4111       2139
## [337,]  13970  1511    1330    650              146        778
## [338,]   9351  1347    2611   8170              442        868
## [339,]      3   333    7021  15601               15        550
## [340,]   2617  1188    5332   9584              573       1942
## [341,]    381  4025    9670    388             7271       1371
## [342,]   2320  5763   11238    767             5162       2158
## [343,]    255  5758    5923    349             4595       1328
## [344,]   1689  6964   26316   1456            15469         37
## [345,]   3043  1172    1763   2234              217        379
## [346,]   1198  2602    8335    402             3843        303
## [347,]   2771  6939   15541   2693             6600       1115
## [348,]  27380  7184   12311   2809             4621       1022
## [349,]   3428  2380    2028   1341             1184        665
## [350,]   5981 14641   20521   2005            12218        445
## [351,]   3521  1099    1997   1796              173        995
## [352,]   1210 10044   22294   1741            12638       3137
## [353,]    608  1106    1533    830               90        195
## [354,]    117  6264   21203    228             8682       1111
## [355,]  14039  7393    2548   6386             1333       2341
## [356,]    190   727    2012    245              184        127
## [357,]  22686   134     218   3157                9        548
## [358,]     37  1275   22272    137             6747        110
## [359,]    759 18664    1660   6114              536       4100
## [360,]    796  5878    2109    340              232        776
## [361,]  19746  2872    2006   2601              468        503
## [362,]   4734   607     864   1206              159        405
## [363,]   2121  1601    2453    560              179        712
## [364,]   4627   997    4438    191             1335        314
## [365,]   2615   873    1524   1103              514        468
## [366,]   4692  6128    8025   1619             4515       3105
## [367,]   9561  2217    1664   1173              222        447
## [368,]   3477   894     534   1457              252        342
## [369,]  22335  1196    2406   2046              101        558
## [370,]   6211   337     683   1089               41        296
## [371,]  39679  3944    4955   1364              523       2235
## [372,]  20105  1887    1939   8164              716        790
## [373,]   3884  3801    1641    876              397       4829
## [374,]  15076  6257    7398   1504             1916       3113
## [375,]   6338  2256    1668   1492              311        686
## [376,]   5841  1450    1162    597              476         70
## [377,]   3136  8630   13586   5641             4666       1426
## [378,]  38793  3154    2648   1034               96       1242
## [379,]   3225  3294    1902    282               68       1114
## [380,]   4048  5164   10391    130              813        179
## [381,]  28257   944    2146   3881              600        270
## [382,]  17770  4591    1617   9927              246        532
## [383,]  34454  7435    8469   2540             1711       2893
## [384,]   1821  1364    3450   4006              397        361
## [385,]  10683 21858   15400   3635              282       5120
## [386,]  11635   922    1614   2583              192       1068
## [387,]   1206  3620    2857   1945              353        967
## [388,]  20918  1916    1573   1960              231        961
## [389,]   9785   848    1172   1677              200        406
## [390,]   9385  1530    1422   3019              227        684
## [391,]   3352  1181    1328   5502              311       1000
## [392,]   2647  2761    2313    907               95       1827
## [393,]    518  4180    3600    659              122        654
## [394,]  23632  6730    3842   8620              385        819
## [395,]  12377   865    3204   1398              149        452
## [396,]   9602  1316    1263   2921              841        290
## [397,]   4515 11991    9345   2644             3378       2213
## [398,]  11535  1666    1428   6838               64        743
## [399,]  11442  1032     582   5390               74        247
## [400,]   9612   577     935   1601              469        375
## [401,]   4446   906    1238   3576              153       1014
## [402,]  27167  2801    2128  13223               92       1902
## [403,]  26539  4753    5091    220               10        340
## [404,]  25606 11006    4604    127              632        288
## [405,]  18073  4613    3444   4324              914        715
## [406,]   6884  1046    1167   2069              593        378
## [407,]  25066  5010    5026   9806             1092        960
## [408,]   7362 12844   18683   2854             7883        553
## [409,]   8257  3880    6407   1646             2730        344
## [410,]   8708  3634    6100   2349             2123       5137
## [411,]   6633  2096    4563   1389             1860       1892
## [412,]   2126  3289    3281   1535              235       4365
## [413,]     97  3605   12400     98             2970         62
## [414,]   4983  4859    6633  17866              912       2435
## [415,]   5969  1990    3417   5679             1135        290
## [416,]   7842  6046    8552   1691             3540       1874
## [417,]   4389 10940   10908    848             6728        993
## [418,]   5065  5499   11055    364             3485       1063
## [419,]    660  8494   18622    133             6740        776
## [420,]   8861  3783    2223    633             1580       1521
## [421,]   4456  5266   13227     25             6818       1393
## [422,]  17063  4847    9053   1031             3415       1784
## [423,]  26400  1377    4172    830              948       1218
## [424,]  17565  3686    4657   1059             1803        668
## [425,]  16980  2884   12232    874             3213        249
## [426,]  11243  2408    2593  15348              108       1886
## [427,]  13134  9347   14316   3141             5079       1894
## [428,]  31012 16687    5429  15082              439       1163
## [429,]   3047  5970    4910   2198              850        317
## [430,]   8607  1750    3580     47               84       2501
## [431,]   3097  4230   16483    575              241       2080
## [432,]   8533  5506    5160  13486             1377       1498
## [433,]  21117  1162    4754    269             1328        395
## [434,]   1982  3218    1493   1541              356       1449
## [435,]  16731  3922    7994    688             2371        838
## [436,]  29703 12051   16027  13135              182       2204
## [437,]  39228  1431     764   4510               93       2346
## [438,]  14531 15488   30243    437            14841       1867
## [439,]  10290  1981    2232   1038              168       2125
## [440,]   2787  1698    2510     65              477         52
predict(wholesale_pca)[,1]
##   [1]  -0.19707283  -0.45313294  -0.81180172   0.79342916  -0.11570147
##   [6]   0.14370629   0.32567049  -0.15665440   0.48890741  -1.62027497
##  [11]  -0.66758413   0.92597350  -0.92658585  -0.82672223  -0.80858534
##  [16]   0.93709140  -0.60479469   0.33914993  -0.29126066   0.29954840
##  [21]   0.33682556   1.09654804   0.26619036  -4.58054505  -1.19755447
##  [26]   0.15537156   1.03266607   1.09811094  -3.14687957   0.88052223
##  [31]  -0.05215116   0.69579690   0.98632753   0.41807632   1.02591988
##  [36]  -0.21643153   0.24158323  -0.97020398  -1.62332525   0.95272626
##  [41]   0.08308879   0.25869103  -0.87588116  -2.00255094  -0.30164586
##  [46]  -2.83141245  -1.90336183  -9.41725404  -0.44041724  -3.63590895
##  [51]   0.91517116   0.47041131   0.34153413  -0.75096260   1.02036283
##  [56]   0.48573185  -4.63920836  -0.95925425   1.08902399   0.02055344
##  [61]   0.20266611  -8.37149191  -0.04643766  -1.44256223   0.84129649
##  [66]  -5.88216805   0.42975520  -0.59711484   0.22115034   1.02170230
##  [71]   0.84070633  -1.73915275   0.62067938   0.26682334  -0.04638691
##  [76]   1.20012549   0.54017219  -2.77004981   1.12399443   0.65209963
##  [81]   1.03868601  -1.10479248  -0.56696336   1.03054389   0.39812160
##  [86] -12.68123458  -8.39266413  -0.92068706   1.01342557   0.44301966
##  [91]   1.19321062   0.80614475  -5.24057761   0.52578694  -0.79761716
##  [96]   0.71560919   0.24404605   1.32938626   1.32246301   1.02727861
## [101]  -1.13082005  -1.34423210  -0.21246138   0.06820127   0.80468449
## [106]   0.94469735  -0.66901612  -1.47652662  -0.04077613  -1.70666698
## [111]   0.99983015  -1.37687414   0.68923179   0.90109151   1.05901888
## [116]   1.05586310   0.94497402   0.63888952   0.94868598   0.98250864
## [121]   0.96940760   1.00153477   1.28120984  -0.18913115   0.86596557
## [126]   0.40917867   1.01779186  -0.30277111   0.39288434   1.02620109
## [131]   1.00675513   1.30343896   0.95838681   1.18401500   1.07458712
## [136]   1.08937421  -0.11183011   0.20888553   0.47286002   0.67212442
## [141]   0.28796809  -0.02250288   0.34418432   1.07654549   0.93281684
## [146]  -3.18443785   1.06717252   0.80824332   1.22430136   1.05447741
## [151]   1.04333128   0.84943798   1.02940017   0.39707127   1.38885601
## [156]  -2.10534411  -0.94690511   0.99393880  -0.28531006  -1.03017136
## [161]  -0.35485260   1.14689210   0.92036981  -3.05168162  -0.14994267
## [166]  -1.80878413  -0.54851470   0.71052625   1.24301618   1.12716773
## [171]  -0.90926104  -3.27135965   0.20685284  -1.58573375   0.83240063
## [176]  -0.53378209   0.23300367   0.34523774   0.52247477   0.63766473
## [181]   0.01290303  -3.32956183  -0.68822721  -7.47744667   1.00703448
## [186]   0.81312626   1.11229463  -0.24041783  -0.72607631  -0.78285913
## [191]   0.74272114   1.27769586   1.09693599  -0.81285702   1.00169591
## [196]   0.45245343   0.08628883  -0.39085008   0.66997842   1.02565202
## [201]  -2.23900996  -2.99546346  -0.68180673   1.10109815   0.89280368
## [206]  -2.04834810   1.22289397   0.02999763   0.29338844  -2.07821189
## [211]   0.95666185  -5.65091274   1.01303835  -0.07733767  -0.54162222
## [216]  -1.23239191  -3.65784251   1.03509689  -1.19058168   1.25137280
## [221]   1.16786662  -0.30619270   1.02353682   0.64173440   1.19242546
## [226]   0.74927539  -0.04166179   1.03747427   0.74782120   0.82806814
## [231]   0.25762310   0.14712185   0.92806057   0.77748264   0.67882658
## [236]   0.58424690   1.07019195   0.93984852   1.29676093   0.65211081
## [241]   0.35751675   0.96409594   1.02852505   0.42242573  -0.37409228
## [246]  -1.17838892   0.99935781   1.26979462   0.74868436   0.81396957
## [251]   1.04468274  -5.00768849   0.74545878  -0.38605647  -0.70708219
## [256]   1.18411490   0.63210547   0.60371331   0.51724649   0.38236102
## [261]   0.77157492   1.16886889   1.08603962   0.50559973  -1.05801199
## [266]  -1.65734964  -1.47739059   0.72868453  -1.21350291   1.23813362
## [271]   1.19514203   0.78067858   0.26602762   0.86878444   0.97282972
## [276]   1.22069804   0.38108645   1.07846333   0.87750350  -0.22439955
## [281]   0.92072808   0.04172049   0.56179348   0.77559110  -0.05666773
## [286]   1.07514112   0.99534417   0.87483219   1.19971862   1.33657531
## [291]   0.83674885   0.85316130   0.69360374  -0.93965965   0.59455930
## [296]   0.66171399   0.90049568   0.25180413  -0.16562608   1.15462330
## [301]   0.06749116  -1.87238584  -0.36075328  -0.89344120  -2.24170924
## [306]  -0.57018410  -1.88935546   0.92559692   1.05503352  -1.82444685
## [311]   0.91380091   0.64646544  -2.05651935   1.10515579   0.58629339
## [316]  -1.18632311   1.04565960   0.55882703   0.88204365  -3.11235419
## [321]   0.88439078   0.80386112   0.92745036   0.37271862   0.85971976
## [326]  -1.78946833   1.05267151   1.17723864   0.81408444   0.85138951
## [331]   0.81990469  -2.55569469   0.81764691  -7.61379702   0.73733540
## [336]  -0.43016311   1.12215088   0.95236916   0.77302224   0.67925139
## [341]  -0.44952190  -0.49874907  -0.03297929  -2.53250139   1.13340753
## [346]   0.22596844  -0.94277386  -0.52623469   0.89883641  -2.40481023
## [351]   1.08068712  -2.45061408   1.19422964  -1.46109306   0.29654054
## [356]   1.19246382   1.30670647  -0.84837304  -0.53430822   0.74548879
## [361]   0.95060230   1.24298882   1.04927604   0.87486904   1.13722957
## [366]  -0.34134077   1.06478454   1.23457189   1.09202865   1.29790056
## [371]   0.54728205   0.92861428   0.55848361  -0.01036762   1.02837629
## [376]   1.15932849  -0.77356526   0.88358086   0.93923945   0.27600519
## [381]   1.07810889   0.81131596  -0.12863861   0.98212572  -1.64808006
## [386]   1.10233193   0.82259230   1.04129188   1.19768522   1.09437876
## [391]   1.06891237   0.88438236   0.79981986   0.48759544   1.07628493
## [396]   1.08292394  -0.65441107   1.06672699   1.21812567   1.20418087
## [401]   1.12755720   0.78619937   0.70963764   0.21181784   0.65039342
## [406]   1.13695208   0.43799628  -1.67259278   0.36550163   0.05904374
## [411]   0.58114647   0.54871526   0.02754893   0.18022987   0.84472130
## [416]  -0.15011103  -0.94319868  -0.17681577  -1.21247875   0.67045226
## [421]  -0.70505273  -0.06490484   0.82591686   0.57180936   0.04046836
## [426]   0.76883248  -0.93848842  -0.43132555   0.51934102   0.83217183
## [431]  -0.12732308   0.28430937   0.83664364   0.89763536   0.27267232
## [436]  -0.78171970   1.00383404  -3.47543102   0.91187529   1.06427400
#The aboved two gives us the same thing. predict is a good function to know.
wholesale$Channel <- as.factor(wholesale$Channel)
out <- sapply(1:5, function(i){plot(wholesale$Channel,wholesale_pca$x[,i],xlab=paste("PC",i,sep=""),ylab="Channel")})

pairs(wholesale_pca$x[,1:5], ylim = c(-6,4),xlim = c(-6,4),panel=function(x,y,...){text(x,y,wholesale$Channel)})

# Better Ways to Visualize

library(factoextra)
## Welcome! Want to learn more? See two factoextra-related books at https://goo.gl/ve3WBa
library(FactoMineR)
library(ggfortify)
library(psych)
## 
## Attaching package: 'psych'
## The following objects are masked from 'package:ggplot2':
## 
##     %+%, alpha
## The following object is masked from 'package:car':
## 
##     logit
library(corrplot)
## corrplot 0.92 loaded
library(devtools)
## Loading required package: usethis
# Correlation
pairs.panels(wholesale[,-1],
             gap = 0,
             bg = c("red", "blue")[wholesale$Channel],
             pch=21)

pairs.panels(wholesale_pca$x,
             gap=0,
             bg = c("red", "blue")[wholesale$Channel],
             pch=21)

fviz_eig(wholesale_pca, addlabels = TRUE)

fviz_pca_var(wholesale_pca,col.var = "cos2",
             gradient.cols = c("#FFCC00", "#CC9933", "#660033", "#330033"),
             repel = TRUE)

fviz_pca_ind(wholesale_pca, col.ind = "cos2", 
                  gradient.cols = c("#FFCC00", "#CC9933", "#660033", "#330033"), 
                  repel = TRUE)

biplot(wholesale_pca)

autoplot(wholesale_pca,
         data = wholesale[,-1],
         loadings = TRUE,
         labels = wholesale$Channel)

# Different PCA Method. 
res.pca <- PCA(wholesale[,-1], graph = FALSE)
print(res.pca)
## **Results for the Principal Component Analysis (PCA)**
## The analysis was performed on 440 individuals, described by 6 variables
## *The results are available in the following objects:
## 
##    name               description                          
## 1  "$eig"             "eigenvalues"                        
## 2  "$var"             "results for the variables"          
## 3  "$var$coord"       "coord. for the variables"           
## 4  "$var$cor"         "correlations variables - dimensions"
## 5  "$var$cos2"        "cos2 for the variables"             
## 6  "$var$contrib"     "contributions of the variables"     
## 7  "$ind"             "results for the individuals"        
## 8  "$ind$coord"       "coord. for the individuals"         
## 9  "$ind$cos2"        "cos2 for the individuals"           
## 10 "$ind$contrib"     "contributions of the individuals"   
## 11 "$call"            "summary statistics"                 
## 12 "$call$centre"     "mean of the variables"              
## 13 "$call$ecart.type" "standard error of the variables"    
## 14 "$call$row.w"      "weights for the individuals"        
## 15 "$call$col.w"      "weights for the variables"
# Visualize and Interpret PCA using these functions 

#get_eigenvalue(res.pca): Extract the eigenvalues/variances of principal components
#fviz_eig(res.pca): Visualize the eigenvalues
#get_pca_ind(res.pca), get_pca_var(res.pca): Extract the results for individuals and variables, respectively.
#fviz_pca_ind(res.pca), fviz_pca_var(res.pca): Visualize the results individuals and variables, respectively.
#fviz_pca_biplot(res.pca): Make a biplot of individuals and variables.

eig.val <- get_eigenvalue(res.pca)
eig.val
##       eigenvalue variance.percent cumulative.variance.percent
## Dim.1 2.64497357        44.082893                    44.08289
## Dim.2 1.70258397        28.376400                    72.45929
## Dim.3 0.74006477        12.334413                    84.79371
## Dim.4 0.56373023         9.395504                    94.18921
## Dim.5 0.28567634         4.761272                    98.95048
## Dim.6 0.06297111         1.049519                   100.00000
fviz_eig(res.pca, addlabels = TRUE, ylim = c(0, 50))

var <- get_pca_var(res.pca)
#var$coord: coordinates of variables to create a scatter plot
#var$cos2: represents the quality of representation for variables on the factor map. It’s calculated as the squared coordinates: var.cos2 = var.coord * var.coord.
#var$contrib: contains the contributions (in percentage) of the variables to the principal components. 
#The contribution of a variable (var) to a given principal component is (in percentage) : (var.cos2 * 100) / (total cos2 of the component).
var
## Principal Component Analysis Results for variables
##  ===================================================
##   Name       Description                                    
## 1 "$coord"   "Coordinates for the variables"                
## 2 "$cor"     "Correlations between variables and dimensions"
## 3 "$cos2"    "Cos2 for the variables"                       
## 4 "$contrib" "contributions of the variables"
# Coordinates
head(var$coord)
##                       Dim.1      Dim.2       Dim.3       Dim.4       Dim.5
## Fresh            0.06974378  0.6888622  0.69876010 -0.17770820  0.02602031
## Milk             0.88654635  0.1085197 -0.05194998 -0.06546390 -0.44179588
## Grocery          0.94206631 -0.1906204  0.09323953  0.07957747  0.16836310
## Frozen           0.08324992  0.7976140 -0.15346028  0.57714209  0.01492942
## Detergents_Paper 0.89227411 -0.3330361  0.11716213  0.12894882  0.18153322
## Delicassen       0.40444082  0.6579050 -0.45069909 -0.41450107  0.16820333
# Cos2: quality on the factore map
head(var$cos2)
##                        Dim.1      Dim.2       Dim.3       Dim.4        Dim.5
## Fresh            0.004864195 0.47453114 0.488265675 0.031580205 0.0006770567
## Milk             0.785964426 0.01177653 0.002698800 0.004285523 0.1951835958
## Grocery          0.887488938 0.03633613 0.008693611 0.006332574 0.0283461332
## Frozen           0.006930549 0.63618812 0.023550058 0.333092988 0.0002228875
## Detergents_Paper 0.796153084 0.11091307 0.013726964 0.016627799 0.0329543113
## Delicassen       0.163572380 0.43283898 0.203129666 0.171811138 0.0282923595
# Contributions to the principal components
head(var$contrib)
##                       Dim.1      Dim.2      Dim.3      Dim.4       Dim.5
## Fresh             0.1839034 27.8712328 65.9760729  5.6020067  0.23700133
## Milk             29.7153981  0.6916858  0.3646708  0.7602081 68.32333158
## Grocery          33.5537923  2.1341756  1.1747094  1.1233341  9.92246429
## Frozen            0.2620272 37.3660348  3.1821617 59.0873033  0.07802099
## Detergents_Paper 30.1006064  6.5143964  1.8548328  2.9496021 11.53554083
## Delicassen        6.1842728 25.4224745 27.4475524 30.4775458  9.90364098
#The plot Below is also known as variable correlation plots. It shows the relationships between all variables. It can be interpreted as follow:

#Positively correlated variables are grouped together.
#Negatively correlated variables are positioned on opposite sides of the plot origin (opposed quadrants).
#The distance between variables and the origin measures the quality of the variables on the factor map. 
#Variables that are away from the origin are well represented on the factor map.

# Correlation circle
fviz_pca_var(res.pca, col.var = "black")

# Quality of representation


corrplot(var$cos2, is.corr=FALSE)

# Total cos2 of variables on Dim.1 and Dim.2
#A high cos2 indicates a good representation of the variable on the principal component. 
#In this case the variable is positioned close to the circumference of the correlation circle.
#A low cos2 indicates that the variable is not perfectly represented by the PCs. 
#In this case the variable is close to the center of the circle.

fviz_cos2(res.pca, choice = "var", axes = 1:2)

fviz_pca_var(res.pca, col.var = "cos2",
             gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"), 
             repel = TRUE # Avoid text overlapping
             )

# Change the transparency by cos2 values
fviz_pca_var(res.pca, alpha.var = "cos2")

corrplot(var$contrib, is.corr=FALSE)

# Contributions of variables to PC1
fviz_contrib(res.pca, choice = "var", axes = 1, top = 10)

# Contributions of variables to PC2
fviz_contrib(res.pca, choice = "var", axes = 2, top = 10)

fviz_pca_var(res.pca, col.var = "contrib",
             gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07")
             )

fviz_pca_var(res.pca, alpha.var = "contrib")

fviz_pca_ind(res.pca,
             geom.ind = "point", # show points only (nbut not "text")
             col.ind = wholesale$Channel, # color by groups
             palette = c("#00AFBB", "#E7B800", "#FC4E07"),
             addEllipses = TRUE, # Concentration ellipses
             legend.title = "Groups"
             )

# Description of PC

res.desc <- dimdesc(res.pca, axes = c(1,2,3,4,5), proba = 0.05)
# Description of dimension 1
res.desc$Dim.1
## 
## Link between the variable and the continuous variables (R-square)
## =================================================================================
##                  correlation       p.value
## Grocery            0.9420663 6.584197e-210
## Detergents_Paper   0.8922741 2.332450e-153
## Milk               0.8865463 1.021905e-148
## Delicassen         0.4044408  9.572010e-19
res.desc$Dim.2
## 
## Link between the variable and the continuous variables (R-square)
## =================================================================================
##                  correlation      p.value
## Frozen             0.7976140 3.240676e-98
## Fresh              0.6888622 3.479571e-63
## Delicassen         0.6579050 6.655870e-56
## Milk               0.1085197 2.281127e-02
## Grocery           -0.1906204 5.720097e-05
## Detergents_Paper  -0.3330361 7.407426e-13
res.desc$Dim.3
## 
## Link between the variable and the continuous variables (R-square)
## =================================================================================
##                  correlation      p.value
## Fresh              0.6987601 1.038376e-65
## Detergents_Paper   0.1171621 1.392869e-02
## Frozen            -0.1534603 1.242240e-03
## Delicassen        -0.4506991 2.124105e-23
res.desc$Dim.4
## 
## Link between the variable and the continuous variables (R-square)
## =================================================================================
##                  correlation      p.value
## Frozen             0.5771421 1.940954e-40
## Detergents_Paper   0.1289488 6.759315e-03
## Fresh             -0.1777082 1.790336e-04
## Delicassen        -0.4145011 1.069376e-19
res.desc$Dim.5
## 
## Link between the variable and the continuous variables (R-square)
## =================================================================================
##                  correlation      p.value
## Detergents_Paper   0.1815332 1.287171e-04
## Grocery            0.1683631 3.897641e-04
## Delicassen         0.1682033 3.948465e-04
## Milk              -0.4417959 1.902645e-22
# Graph of Indiviuals
ind <- get_pca_ind(res.pca)
ind
## Principal Component Analysis Results for individuals
##  ===================================================
##   Name       Description                       
## 1 "$coord"   "Coordinates for the individuals" 
## 2 "$cos2"    "Cos2 for the individuals"        
## 3 "$contrib" "contributions of the individuals"
## Principal Component Analysis Results for individuals
##  ===================================================
##   Name       Description                       
## 1 "$coord"   "Coordinates for the individuals" 
## 2 "$cos2"    "Cos2 for the individuals"        
## 3 "$contrib" "contributions of the individuals"
#To get access to the different components, use this:

# Coordinates of individuals
head(ind$coord)
##        Dim.1      Dim.2       Dim.3      Dim.4      Dim.5
## 1  0.1932905 -0.3051000  0.14087845 -0.4864315 -0.4952815
## 2  0.4344199 -0.3284126 -0.31900662 -0.1788304 -0.3655793
## 3  0.8111432  0.8150957 -1.52341562 -1.2540815  0.3790535
## 4 -0.7786478  0.6527537 -0.16301227  0.3800601  0.2761376
## 5  0.1662873  1.2714337 -0.06627939 -0.8262267  0.3942107
## 6 -0.1561699 -0.2951410 -0.14761194 -0.4182883 -0.4794549
# Quality of individuals
head(ind$cos2)
##        Dim.1     Dim.2       Dim.3      Dim.4      Dim.5
## 1 0.05909079 0.1472254 0.031389739 0.37423296 0.38797412
## 2 0.33287156 0.1902379 0.179496780 0.05640788 0.23573307
## 3 0.12102385 0.1222062 0.426886756 0.28928601 0.02642877
## 4 0.47243428 0.3320152 0.020706173 0.11255473 0.05941693
## 5 0.01111679 0.6499033 0.001766112 0.27444781 0.06247669
## 6 0.04507824 0.1610020 0.040273103 0.32338772 0.42488124
# Contributions of individuals
head(ind$contrib)
##         Dim.1      Dim.2       Dim.3      Dim.4      Dim.5
## 1 0.003210312 0.01242576 0.006094902 0.09539365 0.19515389
## 2 0.016216062 0.01439721 0.031251939 0.01289313 0.10632521
## 3 0.056535480 0.08868619 0.712712536 0.63405591 0.11430734
## 4 0.052096452 0.05687711 0.008160527 0.05823452 0.06066302
## 5 0.002375986 0.21578747 0.001349070 0.27521650 0.12363168
## 6 0.002095660 0.01162781 0.006691455 0.07053870 0.18288096
fviz_pca_ind(res.pca)

fviz_pca_ind(res.pca, col.ind = "cos2", 
             gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"),
             repel = TRUE # Avoid text overlapping (slow if many points)
             )

fviz_pca_ind(res.pca, pointsize = "cos2", 
             pointshape = 21, fill = "#E7B800",
             repel = TRUE # Avoid text overlapping (slow if many points)
             )

fviz_pca_ind(res.pca, col.ind = "cos2", pointsize = "cos2",
             gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"),
             repel = TRUE # Avoid text overlapping (slow if many points)
             )

fviz_cos2(res.pca, choice = "ind")

# Total contribution on PC1 and PC2
fviz_contrib(res.pca, choice = "ind", axes = 1:2)

# Create a random continuous variable of length 23,
# Same length as the number of active individuals in the PCA
set.seed(123)
my.cont.var <- rnorm(49)
# Color individuals by the continuous variable


fviz_pca_ind(res.pca,
             geom.ind = "point", # show points only (nbut not "text")
             col.ind = wholesale$Channel, # color by groups
             palette = c("#00AFBB", "#E7B800", "#FC4E07"),
             addEllipses = TRUE, # Concentration ellipses
             legend.title = "Groups"
             )

fviz_pca_ind(res.pca, geom.ind = "point", col.ind = wholesale$Channel, 
             palette = c("#00AFBB", "#E7B800", "#FC4E07"),
             addEllipses = TRUE, ellipse.type = "confidence",
             legend.title = "Groups"
             )

fviz_pca_ind(res.pca,
             label = "none", # hide individual labels
             habillage = wholesale$Channel, # color by groups
             addEllipses = TRUE, # Concentration ellipses
             palette = "jco"
             )

fviz_pca_var(res.pca, geom.var = c("point", "text"))

# Show individuals text labels only
fviz_pca_ind(res.pca, geom.ind =  "text")

# Change the size of arrows an labels
fviz_pca_var(res.pca, arrowsize = 1, labelsize = 5, 
             repel = TRUE)

# Change points size, shape and fill color
# Change labelsize
fviz_pca_ind(res.pca, 
             pointsize = 3, pointshape = 21, fill = "lightblue",
             labelsize = 5, repel = TRUE)

fviz_pca_ind(res.pca,
             geom.ind = "point", # show points only (but not "text")
             group.ind = wholesale$Channel, # color by groups
             legend.title = "Groups",
             mean.point = FALSE)

fviz_pca_ind(res.pca,
             geom.ind = "point", # show points only (but not "text")
             group.ind = wholesale$Channel, # color by groups
             legend.title = "Groups",
             mean.point = TRUE)

fviz_pca_var(res.pca, axes.linetype = "blank")

ind.p <- fviz_pca_ind(res.pca, geom = "point", col.ind = wholesale$Channel)
ggpubr::ggpar(ind.p,
              title = "Principal Component Analysis",
              subtitle = "Wholesale Dataset",
              xlab = "PC1", ylab = "PC2",
              legend.title = "Channel", legend.position = "top",
              ggtheme = theme_gray(), palette = "jco"
              )

fviz_pca_biplot(res.pca, repel = TRUE,col.ind = wholesale$Channel,
                col.var = "#2E9FDF", # Variables color
                )

fviz_pca_biplot(res.pca, 
                col.ind = wholesale$Channel, palette = "jco", 
                addEllipses = TRUE, label = "var",
                col.var = "black", repel = TRUE,
                legend.title = "Channel") 

fviz_pca_biplot(res.pca, 
                # Fill individuals by groups
                geom.ind = "point",
                pointshape = 21,
                pointsize = 2.5,
                fill.ind = wholesale$Channel,
                col.ind = "black",
                # Color variable by groups
                legend.title = list(fill = "Channel", color = "Clusters"),
                repel = TRUE        # Avoid label overplotting
             )+
  ggpubr::fill_palette("jco")+      # Indiviual fill color
  ggpubr::color_palette("npg")      # Variable colors

fviz_pca_biplot(res.pca, 
                # Individuals
                geom.ind = "point",
                fill.ind = wholesale$Channel, col.ind = "black",
                pointshape = 21, pointsize = 2,
                palette = "jco",
                addEllipses = TRUE,
                # Variables
                alpha.var ="contrib", col.var = "contrib",
                gradient.cols = "RdYlBu",
                
                legend.title = list(fill = "Channel", color = "Contrib",
                                    alpha = "Contrib")
                )